一类非线性抛物型方程组解的整体存在及爆破

研究了一类带有非线性边界条件的非线性抛物型方程组解的整体存在及解在有限时刻爆破问题.通过构造方程组的上、下解.得到了解整体存在及解在有限时刻爆破的充分条件.对指数型反应项和边界流采用了常微分方程方法构造其上下解,而其它例如第一特征值等方法运用于该方程就比较困难.     

一类多重耦合变指数抛物方程组的爆破解研究（英文）

在本文中,我们考虑一类具有非标准增长条件的多重耦合热传导方程组的齐次第一初边值问题.首先,我们研究古典解的存在唯一性,其次,我们讨论了解的爆破指标和解的整体存在性质,进一步,我们区分解的同时与不同时爆破现象,有趣的是变指数不仅仅可以区分解的爆破和整体存在而且可以区分解的同时与不同时爆破,最后,对于同时爆破的情形,在对系数和指数做一些合理假设下,我们得到解在区域上每个点都发生爆破的现象.     

具有非局部边界的多孔介质抛物方程组解的整体存在及爆破

研究了一类具有加权非局部边界和非线性内部源的多孔介质抛物型方程组解的整体存在及爆破问题,通过构造方程组的上、下解及引用比较定理,得到了由幂函数和指数函数完全耦合的多孔介质抛物型方程组解的整体存在及解在有限时刻爆破的充分条件,并推广了已有的结果.     

源项耦合的退化抛物型方程组解的爆破和整体存在

本文研究了一类描述可燃混合气体的热传播过程理论的退化抛物型方程组.借助于椭圆问题的特征值与特征函数理论,通过构造不同的上、下解得到了方程组解的整体存在与有限时刻爆破的条件.此结果不仅扩充了只讨论两个函数的半线性问题,并且证明了方程组中的系数ai,边界条件中的权重函数gi(x,y)以及指数li在决定问题解的爆破与否中起着关键的作用.     

具有梯度源项和非线性边界条件的多孔介质方程组解的爆破

该文主要分析下列多孔介质方程组解的爆破现象■其中l,m> 1,Ω?R^N (N≥2)为具有光滑边界的有界区域.通过使用微分不等式技术和最大值原理,给出方程组的解在有限时刻t^*爆破的充分条件,并分别导出了解的爆破时刻t^*及爆破率的上估计.     

具有正边界值的一类退化抛物方程组解的爆破与全局有界

该文研究具有正边界值条件的一类非局部退化抛物型方程组.借助于上下解方法和分段函数,获得了方程组解的全局有界与爆破准则.结果表明,正的边界值ε_0在确定方程组解的爆破中起着关键的作用.     

一类交叉耦合非线性反应扩散方程组的爆破分析

主要研究了具有混合型的多重非线性项的抛物方程组的初边值问题.方程组中的非线性项是幂函数和指数混合型的.这些非线性项组合出了源-流交叉耦合,通过比较原理得到了方程组的上下解,并得到了解有限时刻爆破的临界指标.     

具有吸收项和边界流的非牛顿渗流方程组整体存在解的临界超曲面问题（英文）

在本文中,我们研究一类具有吸收项和耦合边界流的非牛顿渗流方程组问题.通过应用比较原理和构造自相似形式的上、下解,得到整体存在解的临界超曲面以及Fujita爆破指标结果.这些结果完善了发表在"Differential Integral Equations,2014,27:643―658"中的临界爆破Fujita吸收指标问题.     

含梯度项的椭圆方程组的边界爆破解

研究了含梯度项的椭圆方程组的边界爆破解的性质,其中权函数a(x),b(x)为正并且满足一定的条件.利用上下解的方法及比较原则证明了正解的存在性与唯一性,并得到了边界爆破速率的估计.     

可压缩量子Navier-Stokes方程组光滑解的爆破

本文研究多维可压缩量子Navier-Stokes方程组Cauchy问题光滑解的爆破现象.不同于经典Navier-Stokes方程组光滑解的爆破结果,在一些初始值的合理限制下,本文证明对任意大于1的绝热指数,当黏性系数相对于Planck常数较小时,可压缩量子Navier-Stokes方程组光滑解在有限时刻爆破.     

Blow-Up Behaviors of Solutions to Reaction-Diffusion Equations With Nonlocal Sources and Variable Exponents北大核心CSCD

该文考虑了一类带有变指数非局部项的反应扩散方程的爆破问题。首先,由不动点原理,证明了问题解的局部存在性和唯一性。其次,利用上下解方法,给出在齐次Dirichlet边界条件下,问题的解在有限时间发生爆破的充分条件,即变指数大于零且初始值足够大,并对爆破时间的上下界进行了估计。     

Fujita exponents for a space–time weighted parabolic problem in bounded domains

This paper deals with a semilinear weighted parabolic problem in general bounded domains, subject to zero Dirichlet boundary conditions, where the weighted functions depend not only on space variable but also on time variable. Fujita exponents for blow-up and global existence of solutions are determined by using semigroup methods and the comparison principle, which are composed by the dimensions of the space domains and the eight exponents in nonlinear coupled sources and the space–time weighted functions.     

Existence and Blow-up of Solutions for a Nonlinear Parabolic System with Variable Exponents

In this paper, we study a nonlinear parabolic system with variable exponents. The existence of classical solutions to an initial and boundary value problem is obtained by a fixed point theorem of the contraction mapping, and the blow-up property of solutions in finite time is obtained with the help of the eigenfunction of the Laplace equation and a delicate estimate.     

Asymptotic analysis for blow-up solutions in parabolic equations involving variable exponents

In this article, we consider non-negative solutions of the homogeneous Dirichlet problems of parabolic equations with local or nonlocal nonlinearities, involving variable exponents. We firstly obtain the necessary and sufficient conditions on the existence of blow-up solutions, and also obtain some Fujita-type conditions in bounded domains. Secondly, the blow-up rates are determined, which are described completely by the maximums of the variable exponents. Thirdly, we show that the blow-up occurs only at a single point for the equations with local nonlinearities, and in the whole domain for nonlocal nonlinearities.     

Uniform Blow-up Behavior for Degenerate and Singular Parab olic Equations

This paper deals with the degenerate and singular parabolic equations coupled via nonlinear nonlocal reactions, subject to zero-Dirichlet boundary conditions. After giving the existence and uniqueness of local classical nonnegative solutions, we show critical blow-up exponents for the solutions of the system. Moreover, uniform blow-up behaviors near the blow-up time are obtained for simultaneous blow-up solutions, divided into four subcases.     

Blow-up properties in the parabolic problems with anisotropic nonstandard growth conditions

In this paper, we study the parabolic problems with anisotropic nonstandard growth nonlinearities. We first give the existence and uniqueness of weak solutions in variable Sobolev spaces. Second, we use the energy methods to show the existence of blow-up solutions with negative or positive initial energy, respectively. Both the variable exponents and the coefficients make important roles in Fujita blow-up phenomena. Moreover, asymptotic properties of the blow-up solutions are determined.     

Critical Fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux

We establish the critical Fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux and then determine the blow-up rates and the blow-up sets for the nonglobal solutions.     

退化和奇异抛物系统的一致爆破行为（英文）

This paper deals with the degenerate and singular parabolic equations coupled via nonlinear nonlocal reactions, subject to zero-Dirichlet boundary conditions. After giving the existence and uniqueness of local classical nonnegative solutions, we show critical blowup exponents for the solutions of the system. Moreover, uniform blow-up behaviors near the blow-up time are obtained for simultaneous blow-up solutions, divided into four subcases.     

Blow-up time and boundary layer for solutions in parabolic equations with different diffusion

This paper deals with parabolic equations with different diffusion coefficients and coupled nonlinear sources, subject to homogeneous Dirichlet boundary conditions. We give many results about blow-up solutions, including blow-up time estimates for all of the spatial dimensions, the critical non-simultaneous blow-up exponents, uniform blow-up profiles, blow-up sets, and boundary layer with or without standard conditions on nonlocal sources. The conditions are much weaker than the ones for the corresponding results in the previous papers.     

Asymptotic properties of singular solutions in degenerate parabolic equation with boundary flux

ABSTRACT

This paper deals with blow-up and quenching solutions of degenerate parabolic problem involving m-Laplacian operator and nonlinear boundary flux. The blow-up and quenching criteria are classified under the conditions on the initial data but with less conditions on the relationship among the exponents, respectively. Moreover, asymptotic properties including singular rates, set and time estimates are determined for the blow-up solutions and the quenching solutions, respectively.