对高维热粘弹方程组解的整体存在性的注记

In this paper, we obtain some global existence results for the higher-dimensional nonhomogeneous, linear, semilinear and nonlinear thermoviscoelastic systems by using semi-group approach.     

一维非单调流体模型在H2中解的整体存在性

In this paper, we prove the existence in H_ ~2, an incomplete metric subspace of H~2×H~2×H~2, of global solutions to the system for a one-dimensional non-monotone fluid in bounded domainΩ=(0,1). The results in this paper have improved those previously related results.     

关于非线性波动方程经典解整体存在性的一个注记

本文和文[1]一起,对具一般形式非线性右端项的非线性波动方程的柯西问题的整体经典解的存在唯一性,给出了[1]中所述结果的完整的证明。     

非线性非单调算子方程的解

该文研究了一类非线性，非单调算子方程x＝A（x，x）的解的存在性及唯一性，推广并改进了若干已知结果．     

非线性一维热粘实际气体方程组解的整体存在性和渐近性

本文证明了一类非线性热传导一维粘性实际气体方程组解的繁体存在性和渐近性,并证明了当t→＋∞时,此整体解趋于其相应稳态问题的解,另外,本文渐近性结果改进了[22]中的结果,而且[8]中结果是本文部分结果的特例。     

非线性波动方程经典解的整体存在性

该文证明了波动方程uu－△u＝F（u，Du）的Cauchy问题整体经典解的存在性唯一性，并对方程中出现的每项u，Du，D2u的某种范数均得到了与齐次方程相同的衰减估计，其结果补充和丰富了[4]中F不显含u时的结果．     

具有多重非线性的非牛顿多方渗流方程的整体存在性与非存在性

考虑了一个具有多重非线性的抛物模型中,非线性扩散项、非线性反应项和非线性边界流三种非线性机制之间的相互作用.通过构造自相似上解和自相似下解,获得了临界整体存在性曲线和临界Fujita曲线.     

半线性热方程整体解的存在性与非存在性

本文研究半线性热方程的初值问题ｕｔ－Δｕ＝ｕγ（γ＞１），ｕ（ｘ，０）＝φ（ｘ）的非负古典解与Ｌｐ解的整体存在性、非存在性与ｂｌｏｗ－ｕｐ．首先，利用归一化的高斯函数得到了一些新的解的非整体存在的充分条件，这些条件对古典解与Ｌｐ解是普遍适用的；然后又讨论了某些非负整体解的存在性．本文不但得到了一些新的结果，而且还简化和统一了某些已知结果的证明．     

具有非线性阻尼项和源项的波动方程整体解的存在性

在初始能量为负的条件下,基于Young不等式,本文证明了一类带耗散项的非线性双曲型方程初边值问题解的blow-up.     

一具有阻尼非线性双曲型方程初边值问题整体解的不存在性

本文证明一具有阻尼非线性双曲型方程初边值问题局部广义解的存在性和唯一性,并给出此问题解爆破的充分条件.     

A Remark on Global Existence in H^4 for a Nonlinear Thermoviscoelasticity Equations with Non-monotone Pressure

We consider a one-dimensional continuous model of nutron star,described by a compressible thermoviscoelastic system with a non-monotone equation of state,due to the effective Skyrme nuclear interaction between particles.We will prove that,despite a possible, destabilizing influence of the pressure,which is non-monotone and not always positive,the presence of viscosity and a sufficient thermal dissipation dcscribc the global existence of solutions in H~4 with a mixed free boundary problem for our model.     

Global Existence in H^2 for a 1-d Non-monotone Fluid

In this paper, we prove the existence in H＋^2, an incomplete metric subspace of H^2×H^2×H^2, of global solutions to the system for a one-dimensional non-monotone fluid in bounded domainΩ=（0,1）. The results in this paper have improved those previously related results.     

Global Existence for a Class of Non-Fickian Polymer-penetrant Systems

This paper deals with a class of strongly coupled and highly degenerate nonlinear parabolic systems, which arises from a model describing non-Fickian diffusion of penetrant into glassy polymers. By means of a fixed point argument and a priori estimates, we establish the global existence and uniqueness for the systems.     

The Global Existence of Solutions for a Cross-diffusion System

This paper is concerned with the global existence of solutions for a class of quasilinear cross-diffusion system describing two species competition under self and cross population pressure. By establishing and using more detailed interpolation results between several different Banach spaces, the global existence of solutions are proved when the self and cross diffusion rates for the first species are positive and there is no self or cross-diffusion for the second species.     

一类非线性算子方程解存在性的注记

利用不动点指数理论,讨论了非线性算子方程Ax=μx解的存在性并给出了方程解的存在性定理,推广了某些文献已有的结果.     

Existence of a Global Solution to One Model Problem of Atmosphere Dynamics

We consider a model problem of compressible viscous fluid dynamics in the two-dimensional case. We prove a global existence theorem.     

带Robin边界条件的拟线性抛物方程解的整体存在性与爆破

主要研究了一类带Robin边界条件的拟线性抛物方程解的整体存在性与爆破问题,利用微分不等式技术,获得了方程的解发生爆破时的爆破时间的下界.然后给出了方程解整体存在的充分条件,最后得到了方程的解发生爆破时发生爆破时间的上界.     

Global Existence and Blow-up for a Parabolic System with Nonlinear Boundary Conditions

This paper deals with the global existence and blow-up of positive solutions to the systems: u_t = ∇(u^∇u) + u¹ + v^a v_t = ∇(v^n∇v) + u^b + v^k in B_R × (0, T) \frac{∂u}{∂η} = u^αv^p, \frac{∂v}{∂η} = u^qv^β on S_R × (0, T) u(x, 0) = u_0(x), v(x, 0} = v_0(x) in B_R We prove that there exists a global classical positive solution if and only if l ≤ l, k ≤ 1, m + α ≤ 1, n + β ≤ 1, pq ≤ (1 - m - α)(1 - n - β),ab ≤ 1, qa ≤ (1 - n - β) and pb ≤ (1 - m - α).