具有空变系数的半线性反应-扩散抛物系统在非线性边界条件下解的爆破时间的下界

研究了高维空间上具有空变系数的半线性反应-扩散抛物系统在非线性边界条件下的解的爆破问题.构造了一个能量表达式,运用微分不等式的方法,得到了该能量方程所满足的微分不等式.然后通过积分导出了解的爆破时间下界的估计.     

非线性边界条件下具有空变系数和吸收项的非局部多孔介质抛物方程解的爆破现象

本文研究了非线性边界条件下具有空变系数和吸收项的非局部多孔介质抛物方程解的爆破问题.运用微分不等式技巧,得到了高维空间上非线性边界条件下具有空变系数和吸收项的非局部多孔介质抛物方程全局解的条件.同时,通过构造能量表达式,应用Sobolev不等式等技巧,推出了爆破发生时解的爆破时间上界和下界估计.     

一类具有Dirichlet边界条件的反应扩散方程的爆破解

针对一类具有Dirichlet边界条件的非线性反应扩散方程的爆破问题,通过构造恰当的辅助函数和利用一阶微分不等式技术,给出了解在有限时刻爆破的一个充分条件,并在一定条件下得到了爆破时刻的上界和下界.     

一类非线性反应扩散方程在高维空间的爆破解

主要讨论了一类具有Dirichlet边界条件的非线性反应扩散方程在高维空间的爆破解.通过构造恰当的辅助函数和利用一阶微分不等式技术,给出了在高维空间下爆破解存在的充分条件以及爆破时刻的上下界.     

非线性边界条件下高维拋物方程解的全局存在性及爆破现象

该文研究了非线性边界条件下高维空间上更一般化的非线性抛物问题解的爆破现象以及全局解的存在性.通过构造辅助函数,并对方程中的已知数据项进行一些必要的假设,应用微分不等式技术,当爆破发生时推导了爆破时间的下界.也推到了方程的解一定发生的条件并得到了爆破时间的上界.同时,不管方程对外施力还是受到外力的作用,也研究了方程的解全局存在的条件.     

非线性边界条件下具有变系数的热量方程解的存在性及爆破现象

考虑了定义在Ω上的有变系数的热量方程,其中Ω∝RN(N≥2)是一个有界的凸区域,并且方程具有非线性边界条件.利用微分不等式技术,首先推导了爆破一定发生的条件,并确定了爆破时间的上界.同时,通过对非线性项做一定的限制,得到了解的全局存在性.当爆破发生时,确定了爆破时间的下界.     

一类非线性抛物系统解的爆破现象

研究了具有依赖于时间的系数的非线性抛物方程解的爆破现象.对已知数据项进行一定的假设并设置一些辅助函数,应用微分不等式技术,得到了方程的解发生爆破的条件.当爆破发生时,分别推导了方程在二维区域和三维区域上解的爆破时间的下界.     

Robin边界条件下更一般化的非线性抛物问题全局解的存在性和爆破

本文主要研究了Robin边界条件下更一般化的非线性抛物问题解的爆破现象以及全局解的存在性.通过对问题中的已知函数进行适当的假设,建立适当的辅助函数,应用微分不等式技术,当问题的解发生爆破时得到了解的爆破时间的下界.这种类型的下界在物理学、生物学、天文学等领域有着广泛的应用.同时,也推导了问题的解全局存在的条件.     

非线性边界条件下抛物问题解的爆破

本文讨论在在非线性边界条件下反应-扩散方程解的爆破.当非线性项f,g满足一定的条件时,我们得到其解在有限时间内爆破.     

具有非局部源的p-Laplace方程解的爆破时间下界估计

该文考虑了三维空间中具有非局部源的p-Laplace方程分别在Dirichlet边界条件和Robin边界条件下解的爆破性质,通过构造辅助函数并利用微分不等式的技巧,得到了两种边界条件下方程解的爆破时间下界估计.另外,给出了方程解在L~2-范数下不会发生爆破的充分条件·     

Energy decay estimates and infinite blow‐up phenomena for a strongly damped semilinear wave equation with logarithmic nonlinear source

This paper deals with the energy decay estimates and infinite blow‐up phenomena for a strongly damped semilinear wave equation with logarithmic nonlinear source term under null Dirichlet boundary condition. By constructing a new family of potential wells, together with logarithmic Sobolev inequality and perturbation energy technique, we establish sufficient conditions to guarantee the solution exists globally or occurs infinite blow‐up and derive the polynomial or exponential energy decay estimates under some appropriate conditions.     

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.     

Blow‐up phenomena for a semilinear parabolic equation with weighted inner absorption under nonlinear boundary flux

Blow‐up phenomena for a nonlinear divergence form parabolic equation with weighted inner absorption term are investigated under nonlinear boundary flux in a bounded star‐shaped region. We assume some conditions on weight function and nonlinearities to guarantee that the solution exists globally or blows up at finite time. Moreover, by virtue of the modified differential inequality, upper and lower bounds for the blow‐up time of the solution are derived in higher dimensional spaces. Three examples are presented to illustrate applications of our results. Copyright © 2016 John Wiley & Sons, Ltd.     

Blow‐up phenomena for a system of semilinear parabolic equations with nonlinear boundary conditions

This paper deals with the blow‐up phenomena for a system of parabolic equations with nonlinear boundary conditions. We show that under some conditions on the nonlinearities, blow‐up occurs at some finite time. We also obtain upper and lower bounds for the blow‐up time when blow‐up occurs. Copyright © 2014 John Wiley & Sons, Ltd.     

非线性Sobolev-Galpern方程解的blow up

本文研究非线性Ｓｏｂｏｌｅｖ－Ｃａｌｐｅｒｎ方程的初边值问题整体解的不存性即解的爆破问题,用能量估计方法并借助于Ｊｅｎｓｅｎ不等式证明了非线性Ｓｏｂｏｌｉｖ－Ｇａｌｐｅｒｎ方程各种初边值问题在某些假设下不存在整体解。     

Uniform decay and blow‐up of solutions for coupled nonlinear Klein–Gordon equations with nonlinear damping terms

In this work, we consider coupled nonlinear Klein–Gordon equations with nonlinear damping terms, in a bounded domain. The decay estimates of the solution are established by using Nakao's inequality. We also prove the blow up of the solution in finite time with negative initial energy. Copyright © 2013 John Wiley & Sons, Ltd.     

Blow up for nonlinear parabolic equations with time degeneracy under dynamical boundary conditions

We study the blow up behaviour of nonlinear parabolic equations including a time degeneracy, under dynamical boundary conditions. For some exponential and polynomial degeneracies, we develop some energy methods and some spectral comparison techniques and derive upper bounds for the blow up times.     

Global existence and bounds for blow‐up time in a class of nonlinear pseudo‐parabolic equations with a memory term

In this article, we consider the initial boundary value problem for a class of nonlinear pseudo‐parabolic equations with a memory term: Under suitable assumptions, we obtain the local and global existence of the solution by Galerkin method. We prove finite‐time blow‐up of the solution for initial data at arbitrary energy level and obtain upper bounds for blow‐up time by using the concavity method. In addition, by means of differential inequality technique, we obtain a lower bound for blow‐up time of the solution if blow‐up occurs.     

Lower bounds for blow-up time in parabolic problems under Neumann conditions

We consider an initial boundary value problem for the semilinear heat equation under homogeneous Neumann boundary conditions in which the solution may blow up in finite time. A lower bound for the blow-up time is determined by means of a differential inequality argument when blow up occurs. Under alternative conditions on the nonlinearity, some additional bounds for blow-up time are also determined.