GLOBAL SOLUTIONS TO 1D COMPRESSIBLE NAVIER-STOKES/ALLEN-CAHN SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND FREE-BOUNDARY

This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.

Variability of the Pacific subtropical cells under global warming in CMIP6 models

The Pacific subtropical cells(STCs)are shallow meridional overturning circulations connecting the tropics and subtropics,and are assumed to be an important driver of the tropical Pacific decadal variability.The variability of STCs under global warming is investigated using multimodal outputs from the latest phase of the Coupled Model Inter-comparison Project(CMIP6)and ocean reanalysis products.Firstly,the volume transport diagnostic analysis is employed to evaluate how coupled models and ocean reanalysis products reproduce interior STC transport.The variation of heat transport by the interior STC under the high-emissions warming scenarios is also analyzed.The results show that the multimodal-mean linear trends of the interior STC transport along 9°S and 9°N are-0.02 Sv/a and 0.04 Sv/a under global warming,respectively,which is mainly due to the combined effect of the strengthened upper oceanic stratification and the weakening of wind field.There is a compensation relationship between the interior STC and the western boundary transport in the future climate,and the compensation relationship of 9°S is more significant than that of 9°N.In addition,compared with ocean reanalysis products,the coupled models tend to underestimate the variability of the interior STC transport convergence,and thus may lose some sea surface temperature(SST)driving force,which may be the reason for the low STC-SST correlation simulated by the model.The future scenario simulation shows that the heat transport of interior STC is weakened under global warming,with a general agreement across models.

A Review on the Global Stratotype Section and Point of the Permian-Triassic Boundary

This paper provides a synthetic review of researches on Meishan Section D, the Global Stratotype Section and Point of the Permian-Triassic Boundary （PTB）. The history of research, geographic and geological setting of the section are briefly introduced. Changhsingian to ＂Griesbachian＂ conodont and ammonoid zonations, the most perfect Permo-Triassic zonations over the world, are presented, with a short discussion on the age of Otoceras, The Changhsingian to ＂Griesbachian＂ strata are subdivided into three 3rd order sequences, and the sedimentary structure of each sequence is indicated. The paper presents a correlation of the Changhsingian to ＂Griesbachian＂ magneetostratigraphy of the Meishan section with the general scale, and informed the negation of a short magnetic reversal at the PTB suggested by Zhu and Liu （1999）. Recent developments of chemostratigraphy of δ^13C and δ^34S are introduced, especially the discovery of more than one negative δ^13C excursions across the PTB. Two important molecular researches reveal the profound changes at the base of eco-system, the microbial catastrophy, and the euxinic conditions in the photic zone during the Permian-Triassic superanoxic event. The paper reports the changes in dating the age of PTB since 2001. According to recent achievements, the age of volcanogenic claybed 25, 14 cm below the PTB, is now set at 252.4±0.3 Ma. A discussion on the eventostratigraphy concludes that, although there is a major event episode at beds 25-26, the events across the PTB at Meishan are multi-episodic and commenced prior to the Event Beds 25-26, thus the possibility that the mass extinction was mainly induced by an exterrestrial impact is largely excluded.

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.

A Candidate Global Stratotype Section and Point for the Precambrian——Cambrian Boundary at Meishucun,Yunnan,China

This paper gives the detail description of Meishucun section , Yunnan , China . By studying biotic characteristics , analyzing isotopic age and comparing with the main Precambrian - Cambrian boundary sections in the world , we construct a global stratotype section and a point for the Precambrian-Cambrian boundary at Meishucun , which are of the convenient assessibility , abundant fossils of diverse groups , continuous sedimentation . perfect outcropping , lock of tectonic and metamorphic alteration , and have been deep studied in all related disciplines of sciences .

GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS TO A NONLOCAL EVOLUTION p-LAPLACE SYSTEM WITH NONLINEAR BOUNDARY CONDITIONS

In this paper, the authors discuss the global existence and blow-up of the solution to an evolution p-Laplace system with nonlinear sources and nonlinear boundary condition. The authors first establish the local existence of solutions, then give a necessary and sufficient condition on the global existence of the positive solution.

GLOBAL NONEXISTENCE FOR A VISCOELASTIC WAVE EQUATION WITH ACOUSTIC BOUNDARY CONDITIONS

This paper deals with a class of nonlinear viscoelastic wave equation with damping and source terms utt-Δu-Δut-Δutt+∫^t0g(t-s)Δu(s)ds+ut|ut|^m2-=u|u|^p-2 with acoustic boundary conditions.Under some appropriate assumption on relaxation function g and the initial data,we prove that the solution blows up in finite time if the positive initial energy satisfies a suitable condition.

Global Solutions for a Strongly-coupled Parabolic System with Initial Boundary Values

In this paper, we consider a strongly-coupled parabolic system with initial boundary values. Under the appropriate conditions, using Gagliard-Nirenberg inequality, Poincaré inequality, Gronwall inequality and imbedding theorem, we obtain the global existence of solutions.

EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTIONS OF THE INITIAL-BOUNDARY VALUE PROBLEM FOR SOME DEGENERATE HYPERBOLIC EQUATION

The author considers the global existence and global nonexistence of the initial-boundary value problem for some degenerate hyperbolic equation of the form utt- div（｜△↓｜^P-2 △↓u）=｜u｜^m u, （x,t）∈[0, ＋∞） ×Ω with p 〉 2 and m 〉 0. He deals with the global solutions by D.H.Sattinger＇s potential well ideas. At the same time, when the initial energy is positive, but appropriately bounded, the global nonexistence of solutions is verified by using the analysis method.

GLOBAL EXISTENCE AND NONEXISTENCE FOR A DOUBLY DEGENERATE PARABOLIC SYSTEM COUPLED VIA NONLINEAR BOUNDARY FLUX

This article deals with the degenerate parabolic system with nonlinear boundary flux. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence curve and the critical Fujita curve for the problem. Especially for the blow-up case, it is rather technical. It comes from the construction of the so-called Zel＇dovich-Kompaneetz-Barenblatt profile

STRAIGHTFORWARD MULTI-SCALE BOUNDARY ELEMENT METHOD FOR GLOBAL/LOCAL MECHANICAL ANALYSIS OF ELASTIC HETEROGENEOUS MATERIAL

A straightforward multi-scale boundary element method is proposed for global and local mechanical analysis of heterogeneous material.The method is more accurate and convenient than finite element based multi-scale method.The formulations of this method are derived by combining the homogenization approach and the fundamental equations of boundary element method.The solution gives the convenient formulations to compute global elastic constants and the local stress field.Finally,two numerical examples of porous material are presented to prove the accuracy and the efficiency of the proposed method.The results show that the method does not require the iteration to obtain the solution of the displacement in micro level.

Global Existence of Solutions of the Gierer-Meinhardt System with Mixed Boundary Conditions

We study the global (in time) existence of nonnegative solutions of the Gierer-Meinhardt system with mixed boundary conditions. In the research, the Robin boundary and Neumann boundary conditions were used on the activator and the inhibitor conditions respectively. Based on the priori estimates of solutions, the considerable results were obtained.

GLOBAL EXISTENCE OF WEAKLY DISCONTINUOUS SOLUTIONS TO A KIND OF MIXED INITIAL-BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS

In this paper, the mixed initial-boundary value problem for general first order quasi- linear hyperbolic systems with nonlinear boundary conditions in the domain D = {（t, x） ｜ t ≥ 0, x ≥0} is considered. A sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution is given.

Global Weak Solutions of Initial Boundary Value Problem for Boltzmann-Poisson System with Absorbing Boundary

This paper deals with the initial boundary value problem for the Boltzmann-Poisson system, which arises in semiconductor physics, with absorbing boundary. The global existence of weak solutions is proved by using the stability of velocity averages and the compactness results on L1-theory under weaker conditons on initial boundary values.

GLOBAL CLASSICAL SOLUTION OF FREE BOUNDARY PROBLEM FOR A COUPLED SYSTEM

A two phase free boundary problem for coupled system including three elliptic equations is considered.The problem comes from the discussion of a growth model of self maintaining protocell in multidimensional case.The global classical solution of the problem with free boundary Γ∶y=g(x,t) between two domains is under search.The global existence and uniqueness of a quasi-stationary problem are proved in multidimensional case.

GLOBAL EXISTENCE AND LARGE TIME BEHAVIOR OF SOLUTION TO REACTING FLOW MODEL WITH BOUNDARY EFFECT

The initial boundary value problem (IBVP) for the 3×3 hyperbolic system of reacting flow with source term proposed by R.J.LeVeque and others (see [8]) is considered.It is shown, in the present paper, that if the initial data are a suitable perturbation of a shiftcd shock profile which is suitably away from the boundary, then there exists a unique smooth solution in R2+ to the IBVP of the 3×3 hyperbolic system, which tends to another shifted shock profile of this system as t →∞.

Monocular Depth Estimation with Sharp Boundary

Monocular depth estimation is the basic task in computer vision.Its accuracy has tremendous improvement in the decade with the development of deep learning.However,the blurry boundary in the depth map is a serious problem.Researchers find that the blurry boundary is mainly caused by two factors.First,the low-level features,containing boundary and structure information,may be lost in deep networks during the convolution process.Second,themodel ignores the errors introduced by the boundary area due to the few portions of the boundary area in the whole area,during the backpropagation.Focusing on the factors mentioned above.Two countermeasures are proposed to mitigate the boundary blur problem.Firstly,we design a scene understanding module and scale transformmodule to build a lightweight fuse feature pyramid,which can deal with low-level feature loss effectively.Secondly,we propose a boundary-aware depth loss function to pay attention to the effects of the boundary’s depth value.Extensive experiments show that our method can predict the depth maps with clearer boundaries,and the performance of the depth accuracy based on NYU-Depth V2,SUN RGB-D,and iBims-1 are competitive.

Two-Dimensional Riemann Problems:Transonic Shock Waves and Free Boundary Problems

We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent developments in the rigorous analysis of two-dimensional(2-D)Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations.In particular,we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.

Construction of Global Weak Entropy Solution of Initial-Boundary Value Problem for Scalar Conservation Laws with Weak Discontinuous Flux

This paper is concerned with the initial-boundary value problem of scalar conservation laws with weak discontinuous flux, whose initial data are a function with two pieces of constant and whose boundary data are a constant function. Under the condition that the flux function has a finite number of weak discontinuous points, by using the structure of weak entropy solution of the corresponding initial value problem and the boundary entropy condition developed by Bardos-Leroux-Nedelec, we give a construction method to the global weak entropy solution for this initial-boundary value problem, and by investigating the interaction of elementary waves and the boundary, we clarify the geometric structure and the behavior of boundary for the weak entropy solution.

一个含抑制剂作用的肿瘤生长模型整体解的存在唯一性

研究一个营养物和抑制物同时存在的非线性血管化肿瘤生长模型.首先运用边界固定法将自由边界问题转化为固定边界上的非线性初边值问题,其次运用抛物型方程的L^(p)理论和Banach不动点定理构造压缩映射,证明该问题局部解的存在唯一性,最后利用变换函数与其原始函数之间的关系,用延拓方法得到整体解的存在唯一性.