拟线性双曲方程的两种Blowup机制

对于一般的初值 ,拟线性双曲方程不一定存在整体经典解 ,若不存在整体经典解 ,则解在有限时间内 blowup。主要考虑几种特殊的 Burgers方程 ,讨论其经典解的存在区间以及解发生 blowup时 ,几何blowup与常微 blowup之间的先后顺序。

可压缩欧拉方程解的blowup现象

考虑带有温度项的可压缩欧拉方程解的大时间行为.通过引入特殊的速度函数u(x,t)=c(t)x+b(t),其中b(t)可看作时间扰动项,得到一类显式光滑解.进而来研究欧拉方程解的blowup现象和整体存在性.

一类四阶非线性波动方程初边值整体解的惟一存在性及其blowup性质

对在研究压缩物质层物理波的传播时所提出的一类四阶非线性波动方程进行了研究,用压缩映射原理和解的延拓方法证明了其初始值整体广义解和整体古典解的存在性与惟一性,同时还讨论了其解的爆破性质.

BLOWUP PROPERTIES FOR A CLASS OF NONLINEAR DEGENERATE DIFFUSION EQUATION WITH NONLOCAL SOURCE

A nonlinear degenerate parabolic equation with nonlocal source was considered. It was shown that under certain assumptions the solution of the equation blows up in finite time and the set of blowup points is the whole region. The integral method is used to investigate the blowup properties of the solution.

CP^n(Q)的加权blowup及陈-阮上同调群

对加权射影空间CPn(Q)进行了加权blowup,分析了blowup后的toric结构和orbifold结构,以及所有twisted sector的变化。用组合论的方法计算了blowup前后每个twisted sector的奇异上同调,并且分析了其陈-阮上同调群的变化。

BLOWUP CRITERION FOR THE COMPRESSIBLE FLUID-PARTICLE INTERACTION MODEL IN 3D WITH VACUUM

In this article, we consider the blowup criterion for the local strong solution to the compressible fluid-particle interaction model in dimension three with vacuum. We establish a BKM type criterion for possible breakdown of such solutions at critical time in terms of both the L^∞ （0, T; L^6）-norm of the density of particles and the ^L1（0, T; L^∞）-norm of the deformation tensor of velocity gradient.

ELASTIC MEMBRANE EQUATION WITH MEMORY TERM AND NONLINEAR BOUNDARY DAMPING:GLOBAL EXISTENCE,DECAY AND BLOWUP OF THE SOLUTION

In this paper we consider the Elastic membrane equation：with memory term and nonlinear boundary damping： Under some appropriate assumptions on the relaxation function h and with certain initial data, the global existence of solutions ：and a general decay for the energy are established using the multiplier technique. Also, ＇we show that a nonlinear source of polynomial type is able to force solutions to blow up in finite time even in presence of a nonlinear damping.

一类退化抛物型方程初边值问题的Blowup

利用Gauss公式和Poincare公式 ,讨论一类退化方程第一类初边值问题解u的爆破性质 ,并对 | u|进行估计。

A NOTE ON GRADIENT BLOWUP RATE OF THE INHOMOGENEOUS HAMILTON-JACOBI EQUATIONS

The gradient blowup of the equation ut = △u ＋ a（x）｜△u｜p ＋ h（x）, where p 〉 2, is studied. It is shown that the gradient blowup rate will never match that of the self-similar variables. The exact blowup rate for radial solutions is established under the assumptions on the initial data so that the solution is monotonically increasing in time.

A blowup criterion for the 3D generalized MHD system with zero magnetic diffusivity

This paper proves a new regularity criterion ω: = rotu∈L1(0,T;B·0∞,∞) for the 3D generalized MHD system with fractional diffusion terms(-Δ)αu with α >9/8 and zero magnetic diffusivity. Here u is the fluid velocity,ω is the vorticity and B·0∞,∞is the homogeneous Besov space.

Finite Time Blowup with Upper Bound of Blowup Time of Solutions to Semilinear Parabolic Equations with General Nonlinearity

In this paper,we consider a semilinear parabolic equation with a general nonlinearity.We establish a new finite time blow-up criterion and also derive the upper bound for the blow-up time.The results partially generalize some recent ones obtained by He Ma et al.

Blowup of Solutions to the Non-Isentropic Compressible Euler Equations with Time-Dependent Damping and Vacuum

This paper mainly studies the blowup phenomenon of solutions to the compressible Euler equations with general time-dependent damping for non-isentropic fluids in two and three space dimensions. When the initial data is assumed to be radially symmetric and the initial density contains vacuum, we obtain that classical solution, especially the density, will blow up on finite time. The results also reveal that damping can really delay the singularity formation.

弱耗散Camassa-Holm方程解的Blowup及衰减性质

本文研究弱耗散Camassa-Holm方程的Cauchy问题,由Kato理论得到了局部适定性的结果,证明了解的blowup及整体存在性,并证明了当耗散系数满足适当条件时,整体解具有衰减性质.

Orbifold Gromov-Witten theory of weighted blowups

Consider a compact symplectic sub-orbifold groupoid S of a compact symplectic orbifold groupoid(X,ω).LetXabe the weight-a blowup of X along S,and Da=PNa be the exceptional divisor,where N is the normal bundle of S in X.In this paper we show that the absolute orbifold Gromov-Witten theory ofXacan be effectively and uniquely reconstructed from the absolute orbifold Gromov-Witten theories of X,S and Da,the natural restriction homomorphism HCR^*(X)→HCR*(S)and the first Chern class of the tautological line bundle over DQ.To achieve this we first prove similar results for the relative orbifold Gromov-Witten theories of(Xa|Da)and(Na|Da).As applications of these results,we prove an orbifold version of a conjecture of Maulik and Pandharipande(Topology,2006)on the Gromov-Witten theory of blowups along complete intersections,a conjecture on the Gromov-Witten theory of root constructions and a conjecture on the Leray-Hirsch result for the orbifold Gromov-Witten theory of Tseng and You(J Pure Appl Algebra,2016).

Blowup Behavior of Solutions to an w-diffusion Equation on the Graph

In this article,we discuss the blowup phenomenon of solutions to the wdiffusion equation with Dirichlet boundary conditions on the graph.Through Banach fixed point theorem,comparison principle,construction of auxiliary function and other methods,we prove the local existence of solutions,and under appropriate conditions the blowup time and blowup rate estimation are given.Finally,numerical experiments are given to illustrate the blowup behavior of the solution.

Global existence and blowup of solutions to a free boundary problem for mutualistic model

This article is concerned with a system of semilinear parabolic equations with a free boundary,which arises in a mutualistic ecological model.The local existence and uniqueness of a classical solution are obtained.The asymptotic behavior of the free boundary problem is studied.Our results show that the free problem admits a global slow solution if the inter-specific competitions are strong,while if the inter-specific competitions are weak there exist the blowup solution and global fast solution.

The Blowup Mechanism of Small Data Solutions for the Quasilinear Wave Equations in Three Space Dimensions

For a class of three-dimensional quasilinear wave equations with small initial data, we give a complete asymptotic expansion of the lifespan of classical solutions, that is, we solve a conjecture posed by John and H rmander. As an application of our result, we show that the solution of three- dimensional isentropic compressible Euler equations with irrotational initial data which are a small perturbation from a constant state will develop singularity in the first-order derivatives in finite time while the solution itself is continuous. Furthermore, for this special case, we also solve a conjecture of Alinhac.

Blowup behaviors for diffusion system coupled through nonlinear boundary conditions in a half space

This paper deals with the blowup estimates near the blowup time for the system of heat equations in a half space coupled through nonlinear boundary conditions. The upper and lower bounds of blowup rate are established. The uniqueness and nonuniqueness results for the system with vanishing initial value are given.

Moving collocation methods for time fractional differential equations and simulation of blowup

A moving collocation method is proposed and implemented to solve time fractional differential equations. The method is derived by writing the fractional differential equation into a form of time difference equation. The method is stable and has a third-order convergence in space and first-order convergence in time for either linear or nonlinear equations. In addition, the method is used to simulate the blowup in the nonlinear equations.

The blowup mechanism for 3-D quasilinear wave equations with small data

For a class of special three-dimensional quasilinear wave equations, we study the blowup mechanism of classical solutions. More precisely, under the nondegenerate conditions, any radially symmetric solution with small initial data is shown to develop singularities in the second order derivaties while the first order derivatives and itself remain continuous, moreover the blowup of solution is of “cusp type”.