期刊文献+
共找到94篇文章
< 1 2 5 >
每页显示 20 50 100
A Formulation of the Porous Medium Equation with Time-Dependent Porosity: A Priori Estimates and Regularity Results
1
作者 Koffi B. Fadimba 《Applied Mathematics》 2024年第10期745-763,共19页
We consider a generalized form of the porous medium equation where the porosity ϕis a function of time t: ϕ=ϕ(x,t): ∂(ϕS)∂t−∇⋅(k(S)∇S)=Q(S).In many works, the porosity ϕis either assumed to be independent of (or to de... We consider a generalized form of the porous medium equation where the porosity ϕis a function of time t: ϕ=ϕ(x,t): ∂(ϕS)∂t−∇⋅(k(S)∇S)=Q(S).In many works, the porosity ϕis either assumed to be independent of (or to depend very little of) the time variable t. In this work, we want to study the case where it does depend on t(and xas well). For this purpose, we make a change of unknown function V=ϕSin order to obtain a saturation-like (advection-diffusion) equation. A priori estimates and regularity results are established for the new equation based in part on what is known from the saturation equation, when ϕis independent of the time t. These results are then extended to the full saturation equation with time-dependent porosity ϕ=ϕ(x,t). In this analysis, we make explicitly the dependence of the various constants in the estimates on the porosity ϕby the introduced transport vector w, through the change of unknown function. Also we do not assume zero-flux boundary, but we carry the analysis for the case Q≡0. 展开更多
关键词 Porous Medium Equation POROSITY Saturation Equation a priori Estimates Regularity Results
下载PDF
A Priori Error Analysis for NCVEM Discretization of Elliptic Optimal Control Problem
2
作者 Shiying Wang Shuo Liu 《Engineering(科研)》 2024年第4期83-101,共19页
In this paper, we propose the nonconforming virtual element method (NCVEM) discretization for the pointwise control constraint optimal control problem governed by elliptic equations. Based on the NCVEM approximation o... In this paper, we propose the nonconforming virtual element method (NCVEM) discretization for the pointwise control constraint optimal control problem governed by elliptic equations. Based on the NCVEM approximation of state equation and the variational discretization of control variables, we construct a virtual element discrete scheme. For the state, adjoint state and control variable, we obtain the corresponding prior estimate in H<sup>1</sup> and L<sup>2</sup> norms. Finally, some numerical experiments are carried out to support the theoretical results. 展开更多
关键词 Nonconforming Virtual Element Method Optimal Control Problem a priori Error Estimate
下载PDF
A Priori and A Posteriori Error Estimates of Streamline Diffusion Finite Element Method for Optimal Control Problem Governed by Convection Dominated Diffusion Equation 被引量:5
3
作者 Ningning Yan Zhaojie Zhou 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2008年第3期297-320,共24页
In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existenc... In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results. 展开更多
关键词 Constrained optimal control problem convection dominated diffusion equation stream-line diffusion finite element method a priori error estimate a posteriori error estimate.
下载PDF
A PRIORI ESTIMATE FOR MAXIMUM MODULUS OF GENERALIZED SOLUTIONS OF QUASI-LINEAR ELLIPTIC EQUATIONS 被引量:1
4
作者 梁延 王向东 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1990年第10期941-953,共13页
Let G he a hounded domain in E Consider the following quasi-linear elliptic equationAlthough the houndedness of generalized solutions of the equation is proved for very general structural conditions, it does not suppl... Let G he a hounded domain in E Consider the following quasi-linear elliptic equationAlthough the houndedness of generalized solutions of the equation is proved for very general structural conditions, it does not supply a priori estimate for maximum modulus of solutions. In this paper an estimate to the maximum modulus is made firstly for a special case of quasi-linear elliptic equations, i.e. the A and B satisfy the following structural conditions 展开更多
关键词 quasi-linear elliptic equations generalized solutions maximum modulus a priori estimate.
下载PDF
A PRIORI ESTIMATES TO THE MAXIMUM MODULUS OF GENERALIZED SOLUTIONS OF A CLASS OF QUASILINEAR ELLIPTIC EQUATIONS WITH ANISOTROPIC GROWTH CONDITIONS 被引量:1
5
作者 梁廷 王向东 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1994年第11期1025-1034,共10页
In this paper we give a priori estimates for the maximum modulus of generalizedsolulions of the quasilinear elliplic equations irith anisotropic growth condition.
关键词 quasilinear elliptic equation. nonstandard growth condition.anisotropic Sobolev space. generalized solution. maximum mod-ulus. a priori estimate
下载PDF
Virtual Element Discretization of Optimal Control Problem Governed by Brinkman Equations
6
作者 Yanwei Li 《Engineering(科研)》 CAS 2023年第2期114-133,共20页
In this paper, we discuss virtual element method (VEM) approximation of optimal control problem governed by Brinkman equations with control constraints. Based on the polynomial projections and variational discretizati... In this paper, we discuss virtual element method (VEM) approximation of optimal control problem governed by Brinkman equations with control constraints. Based on the polynomial projections and variational discretization of the control variable, we build up the virtual element discrete scheme of the optimal control problem and derive the discrete first order optimality system. A priori error estimates for the state, adjoint state and control variables in L<sup>2</sup> and H<sup>1</sup> norm are derived. The theoretical findings are illustrated by the numerical experiments. 展开更多
关键词 Virtual Element Method Optimal Control Problem Brinkman Equations a priori Error Estimate
下载PDF
STABILITY OF THE RAREFACTION WAVE FOR THE GENERALIZED KDV-BURGERS EQUATION 被引量:12
7
作者 王治安 朱长江 《Acta Mathematica Scientia》 SCIE CSCD 2002年第3期319-328,共10页
This paper is concerned with the stability of the rarefaction wave for the generalized KdV-Burgers equation [GRAPHICS] Roughly speaking, under the assumption that u(-) < u(+), the solution u(x, t) to Cauchy problem... This paper is concerned with the stability of the rarefaction wave for the generalized KdV-Burgers equation [GRAPHICS] Roughly speaking, under the assumption that u(-) < u(+), the solution u(x, t) to Cauchy problem (1) satisfying (sup)(x&ISIN;R)\u(x, t) - u(R)(x/t)\ --> 0 as t --> infinity, where u(R)(x/t) is the rarefaction wave of the non-viscous Burgers equation u(t) + f(u)(x) = 0 with Riemann initial data [GRAPHICS] 展开更多
关键词 XdV-Burgers equation rarefaction wave a priori estimate L-2-energy method
下载PDF
COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY,VACUUM AND GRAVITATIONAL FORCE IN THE CASE OF GENERAL PRESSURE 被引量:5
8
作者 姚磊 汪文军 《Acta Mathematica Scientia》 SCIE CSCD 2008年第4期801-817,共17页
This is a continuation of the article(Comm.Partial Differential Equations 26(2001)965).In this article,the authors consider the one-dimensional compressible isentropic Navier-Stokes equations with gravitational fo... This is a continuation of the article(Comm.Partial Differential Equations 26(2001)965).In this article,the authors consider the one-dimensional compressible isentropic Navier-Stokes equations with gravitational force,fixed boundary condition,a general pressure and the density-dependent viscosity coefficient when the viscous gas connects to vacuum state with a jump in density.Precisely,the viscosity coefficient μ is proportional to ρ^θ and 0〈θ〈1/2,where ρ is the density,and the pressure P=P(ρ)is a general pressure.The global existence and the uniqueness of weak solution are proved. 展开更多
关键词 Compressible Navier-Stokes equations VaCUUM a priori estimates a globalweak solution EXISTENCE
下载PDF
The Global Solution for a Class of Dissipative Hasegawa-Mima Equation 被引量:6
9
作者 张瑞凤 李瑞阁 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2005年第4期360-366,共7页
Applying the integral a priori estimates method, the existence and uniqueness ofthe global solution for the dissipative Hasegawa-Mima equation with initial periodic bound-ary condition was proved.
关键词 Hasegawa-Mima equation a priori estimate global solution
下载PDF
EXISTENCE OF PERIODIC SOLUTIONS OF PLANAR SYSTEMS WITH FOUR DELAYS 被引量:3
10
作者 Zhang Zhengqiu Wang ZhichengDept. of Appl. Math.,Hunan Univ.,Changsha 410082. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2001年第4期355-363,共9页
The sufficient condition for the existence of non constant periodic solutions of the following planar system with four delays are obtained:x [FK(W1*1。*3/4]′ 1(t)=-a 0x α 1(t)+a 1f 1(x 1(t-τ 1),x 2... The sufficient condition for the existence of non constant periodic solutions of the following planar system with four delays are obtained:x [FK(W1*1。*3/4]′ 1(t)=-a 0x α 1(t)+a 1f 1(x 1(t-τ 1),x 2(t-τ 2)), x [FK(W1*1。*3/4]′ 2(t)=-b 0x α 2(t)+b 1f 2(x 1(t-τ 3),x 2(t-τ 4)).This approach is based on the continuation theorem of the coincidence degree, and the a priori estimate of periodic solutions. 展开更多
关键词 Planar systems non constant periodic solutions coincidence degree the a priori estimate.
下载PDF
Adaptive Finite Element Method Based on Optimal Error Estimates for Linear Elliptic Problems on Nonconvex Polygonal Domains
11
作者 汤雁 郑璇 《Transactions of Tianjin University》 EI CAS 2002年第4期299-302,共4页
The subject of this work is to propose adaptive finite element methods based on an optimal maximum norm error control estimate.Using estimators of the local regularity of the unknown exact solution derived from comput... The subject of this work is to propose adaptive finite element methods based on an optimal maximum norm error control estimate.Using estimators of the local regularity of the unknown exact solution derived from computed approximate solutions,the proposed procedures are analyzed in detail for a non-trivial class of corner problems and shown to be efficient in the sense that they generate the correct type of refinement and lead to the desired control under consideration. 展开更多
关键词 adaptive finite element method error control a priori error estimate
下载PDF
DECAY ESTIMATES OF PLANAR STATIONARY WAVES FOR DAMED WAVE EQUATIONS WITH NONLINEAR CONVECTION IN MULTI-DIMENSIONAL HALF SPACE 被引量:2
12
作者 范丽丽 刘红霞 尹慧 《Acta Mathematica Scientia》 SCIE CSCD 2011年第4期1389-1410,共22页
This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the multi-dimensional half space R n + : u tt u + u t + divf (u) = 0, t 〉 0, x = (x... This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the multi-dimensional half space R n + : u tt u + u t + divf (u) = 0, t 〉 0, x = (x 1 , x ′ ) ∈ R n + := R + × R n 1 , u(0, x) = u 0 (x) → u + , as x 1 → + ∞ , u t (0, x) = u 1 (x), u(t, 0, x ′ ) = u b , x ′ = (x 2 , x 3 , ··· , x n ) ∈ R n 1 . (I) For the non-degenerate case f ′ 1 (u + ) 〈 0, it was shown in [10] that the above initialboundary value problem (I) admits a unique global solution u(t, x) which converges to the corresponding planar stationary wave φ(x 1 ) uniformly in x 1 ∈ R + as time tends to infinity provided that the initial perturbation and/or the strength of the stationary wave are sufficiently small. And in [10] Ueda, Nakamura, and Kawashima proved the algebraic decay estimates of the tangential derivatives of the solution u(t, x) for t → + ∞ by using the space-time weighted energy method initiated by Kawashima and Matsumura [5] and improved by Nishihkawa [7]. Moreover, by using the same weighted energy method, an additional algebraic convergence rate in the normal direction was obtained by assuming that the initial perturbation decays algebraically. We note, however, that the analysis in [10] relies heavily on the assumption that f ′ (u) 〈 0. The main purpose of this paper isdevoted to discussing the case of f ′ 1 (u b ) ≥ 0 and we show that similar results still hold for such a case. Our analysis is based on some delicate energy estimates. 展开更多
关键词 Damped wave equation planar stationary wave a priori estimates decay rates space-time weighted energy method
下载PDF
UNIQUENESS OF THE INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION 被引量:2
13
作者 Jianli XIANG Guozheng YAN 《Acta Mathematica Scientia》 SCIE CSCD 2021年第3期925-940,共16页
This paper considers the inverse acoustic wave scattering by a bounded penetrable obstacle with a conductive boundary condition.We will show that the penetrable scatterer can be uniquely determined by its far-field pa... This paper considers the inverse acoustic wave scattering by a bounded penetrable obstacle with a conductive boundary condition.We will show that the penetrable scatterer can be uniquely determined by its far-field pattern of the scattered field for all incident plane waves at a fixed wave number.In the first part of this paper,adequate preparations for the main uniqueness result are made.We establish the mixed reciprocity relation between the far-field pattern corresponding to point sources and the scattered field corresponding to plane waves.Then the well-posedness of a modified interior transmission problem is deeply investigated by the variational method.Finally,the a priori estimates of solutions to the general transmission problem with boundary data in L^(p)(δΩ)(1<p<2)are proven by the boundary integral equation method.In the second part of this paper,we give a novel proof on the uniqueness of the inverse conductive scattering problem. 展开更多
关键词 acoustic wave UNIQUENESS mixed reciprocity relation modified interior transmission problem a priori estimates
下载PDF
GLOBAL ASYMPTOTICS TOWARD THE REREFACTION WAVES FOR A PARABOLIC-ELLIPTIC SYSTEM RELATED TO THE CAMASSA-HOLM SHALLOW WATER EQUATION 被引量:2
14
作者 马璇 尹慧 金晶 《Acta Mathematica Scientia》 SCIE CSCD 2009年第2期371-390,共20页
This article is concerned with the global existence and large time behavior of solutions to the Cauchy problem for a parabolic-elliptic system related to the Camassa-Holm shallow water equation {ut+(u^2/2)x+px=ε... This article is concerned with the global existence and large time behavior of solutions to the Cauchy problem for a parabolic-elliptic system related to the Camassa-Holm shallow water equation {ut+(u^2/2)x+px=εuxx, t〉0,x∈R, -αPxx+P=f(u)+α/2ux^2-1/2u^2, t〉0,x∈R, (E) with the initial data u(0,x)=u0(x)→u±, as x→±∞ (I) Here, u_ 〈 u+ are two constants and f(u) is a sufficiently smooth function satisfying f" (u) 〉 0 for all u under consideration. Main aim of this article is to study the relation between solutions to the above Cauchy problem and those to the Riemann problem of the following nonlinear conservation law It is well known that if u_ 〈 u+, the above Riemann problem admits a unique global entropy solution u^R(x/t) u^R(x/t)={u_,(f′)^-1(x/t),u+, x≤f′(u_)t, f′(u_)t≤x≤f′(u+)t, x≥f′(u+)t. Let U(t, x) be the smooth approximation of the rarefaction wave profile constructed similar to that of [21, 22, 23], we show that if u0(x) - U(0,x) ∈ H^1(R) and u_ 〈 u+, the above Cauchy problem (E) and (I) admits a unique global classical solution u(t, x) which tends to the rarefaction wave u^R(x/t) as → +∞ in the maximum norm. The proof is given by an elementary energy method. 展开更多
关键词 Parabolic-elliptic system Camassa-Holm equation energy method a priori estimates
下载PDF
EXISTENCE OF GLOBAL SMOOTH SOLUTION TO INITIAL BOUNDARY VALUE PROBLEM FOR A VISCOELASTIC MODEL WITH RELAXATION 被引量:2
15
作者 阮立志 朱长江 《Acta Mathematica Scientia》 SCIE CSCD 2004年第2期265-274,共10页
This paper is concerned with the initial boundary value problem for a viscoelastic model with relaxation. Under the only assumption that the C^0-norm of the initial data is small, without smallness hypothesis for the ... This paper is concerned with the initial boundary value problem for a viscoelastic model with relaxation. Under the only assumption that the C^0-norm of the initial data is small, without smallness hypothesis for the C^1-norm, the existence of the global smooth solution to the corresponding initial boundary value problem is proved. The analysis is based on some a priori estimates obtained by the 'maximum principle' of first-order quasilinear hyperbolic system. 展开更多
关键词 Viscoelastic model RELaXaTION a priori estimates maximum principle
下载PDF
GLOBAL ATTRACTOR FOR HASEGAWA-MIMA EQUATION 被引量:2
16
作者 张瑞凤 郭柏灵 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第5期567-574,共8页
The long time behavior of solution of the Hasegawa-Mima equation with dissipation term was considered. The global attractor problem of the Hasegawa-Mima equation with initial periodic boundary condition was studied. A... The long time behavior of solution of the Hasegawa-Mima equation with dissipation term was considered. The global attractor problem of the Hasegawa-Mima equation with initial periodic boundary condition was studied. Applying the uniform a priori estimates method, the existence of global attractor of this problem was proved, and also the dimensions of the global attractor was estimated. 展开更多
关键词 Hasegawa-Mima equation a priori estimate global attractor Hausdorff and fractal dimensions
下载PDF
REMARK ON THE BLOW-UP CRITERION OF STRONG SOLUTIONS TO THE NAVIER-STOKES EQUATIONS IN MULTIPLIER SPACES 被引量:1
17
作者 Sadek Gala 《Acta Mathematica Scientia》 SCIE CSCD 2010年第5期1413-1418,共6页
In this note, we prove that Xr (0 〈 r 〈 1) norm of the vorticity controls the blow-up phenomena of strong solutions to the Navier-Stokes equations in R3.
关键词 Navier-Stokes equation blow-up criterion a priori estimates
下载PDF
Global attractor for Hirota equation 被引量:1
18
作者 ZHANG Rui-feng GUO Bo-ling 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2008年第1期57-64,共8页
The long time behavior of solution for Hirota equation with zero order dissipation is studied. The global weak attractor for this system in Hper^k is constructed. And then by exact analysis of the energy equation, it ... The long time behavior of solution for Hirota equation with zero order dissipation is studied. The global weak attractor for this system in Hper^k is constructed. And then by exact analysis of the energy equation, it is shown that the global weak attractor is actually the global strong attractor in Hper^k. 展开更多
关键词 Hirota equation a priori estimate global attractor.
下载PDF
A SUBSOLUTION THEOREM FOR THE MONGE-AMPERE EQUATION OVER AN ALMOST HERMITIAN MANIFOLD
19
作者 Jiaogen ZHANG 《Acta Mathematica Scientia》 SCIE CSCD 2022年第5期2040-2062,共23页
Let Ω⊆M be a bounded domain with a smooth boundary ∂Ω,where(M,J,g)is a compact,almost Hermitian manifold.The main result of this paper is to consider the Dirichlet problem for a complex Monge-Ampère equation on... Let Ω⊆M be a bounded domain with a smooth boundary ∂Ω,where(M,J,g)is a compact,almost Hermitian manifold.The main result of this paper is to consider the Dirichlet problem for a complex Monge-Ampère equation on Ω.Under the existence of a C^(2)-smooth strictly J-plurisubharmonic(J-psh for short)subsolution,we can solve this Dirichlet problem.Our method is based on the properties of subsolutions which have been widely used for fully nonlinear elliptic equations over Hermitian manifolds. 展开更多
关键词 complex Monge-ampere equation almost Hermitian manifold a priori estimate SUBSOLUTION J-plurisubharmonic
下载PDF
H^1 SOLUTIONS FOR A CLASS OF SEMILINEAR PARABOLIC SYSTEMS
20
作者 严国政 《Acta Mathematica Scientia》 SCIE CSCD 1997年第1期91-96,共6页
In this paper, we consider the Cauchy problem of a class of semilinear parabolic system. Firstly, we obtain the local existence of solutions of (1.1),(1.2) in H-1(R(1)), and then we prove the global existence of the s... In this paper, we consider the Cauchy problem of a class of semilinear parabolic system. Firstly, we obtain the local existence of solutions of (1.1),(1.2) in H-1(R(1)), and then we prove the global existence of the solutions in H-1 through a priori estimate. 展开更多
关键词 parabolic system a priori estimate global solution
下载PDF
上一页 1 2 5 下一页 到第
使用帮助 返回顶部