一类弱耗散双组份Hunter-Saxton系统的爆破与爆破率

研究了一类周期弱耗散双组份Hunnter-Saxton系统的爆破现象.首先,给出了此类Hunnter-Saxton系统解的局部适定性及其精确的爆破机制;其次,证明了在一定的初始值下Hunnter-Saxton系统强解的几个爆破结果;最后,给出了HunnterSaxton系统强解的爆破率.     

一类系数依赖于时间的抛物系统解的全局存在性及爆破现象

研究了系数依赖于时间的抛物系统解的爆破现象.应用微分不等式技术,得到了一类系数依赖于时间的抛物系统存在全局解的条件.当系统的数据项满足不同的适当约束条件时,推导了爆破时间的上下界.     

扩散引起的爆破问题

众所周知,在某些条件下常微分方程的解有限时刻爆破,与之相应的带齐次Dirichlet边界条件的反应扩散方程的解整体存在.也就是说,扩散阻止了解有限时刻爆破.一个自然的问题常微分方程的解是否整体存在,而与之相应的带齐次Dirichlet边界条件的反应扩散方程的解是否有限时刻爆破?即扩散能否引起解有限时刻爆破?本文将通过一个简单的例子给此问题一个确切的答案.     

扩散引起的爆破问题

众所周知,在某些条件下常微分方程的解有限时刻爆破,与之相应的带齐次Ｄｉｒｉｃｈｌｅｔ边界条件的反应扩散方程的解整体存在也就是说,扩散阻止了解有限时刻爆破一个自然的问题;常微分方程的解是否整体存在,而与之相应的带齐次Ｄｉｒｉｃｈｌｅｔ边界条件的反应扩散方程的解是否有限时刻爆破？即扩散能否引起解有限时刻爆破？本文将通过一个简单的例子给此问题一个确切的答案     

半线性抛物型方程组解的整体存在性与爆破速率估计

研究了具有非线性热源的半线性抛物型方程组的齐次neumann问题解的爆破性质.利用上下解方法得到了解整体存在的条件与爆破条件,并利用FriedmannMcleod方法建立了爆破速率估计.     

具非局部源项的抛物系统解的整体存在与爆破(英文)

考虑一个具有非局部源项的抛物系统非负解的整体存在与爆破问题,通过使用上下解技术,建立了系统的临界指数,而且,相关的分类是最优与最完全的.     

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.     

关于半线性抛物型方程组解的短破率

本文将对某一类半线性抛物型议程组在解的单点爆破情况下，估计当点邻近短爆点时，解的爆破率。     

具有趋化性的非线性系统的解的爆破性态分析

讨论了一个非线性的抛物-椭圆系统,而该系统来源于生物数学中的一个趋化性模型.主要在Sobolev空间的框架下讨论了系统解的爆破性质,得出结论在二维空间中该系统存在一个门槛值,而该值决定了解全局存在或者是发生爆破.最后利用利亚普诺夫函数、下解爆破等方法给出了定理的证明并得出结论.     

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 of solutions to a degenerate parabolic system with nonlocal sources and nonlocal boundaries

This paper deals with a nonlinear degenerate parabolic system with nonlocal source and nonlocal boundaries. By super-solution, sub-solution and auxiliary functions, a criteria for nonnegative solution of global existence and blow-up in finite time is obtained for this degenerate nonlocal problem. Finally, the blow-up rates of blow-up solutions are also estimated.     

UNIFORM BLOW-UP PROFILES FOR HEAT EQUATIONS WITH COUPLING NONLOCAL SOURCES OF ASYMMETRIC MIXED TYPE NONLINEARITIES＊

This article deals with a nonlocal heat system subject to null Dirichlet boundary conditions,where the coupling nonlocal sources consist of mixed type asymmetric nonlinearities.We at first give the cri...     

Blow-up for a degenerate parabolic equation with nonlocal source and nonlocal boundary

In this article, we investigate the blow-up properties of the positive solutions for a doubly degenerate parabolic equation with nonlocal source and nonlocal boundary condition. The conditions on the existence and nonexistence of global positive solutions are given. Moreover, we give the precise blow-up rate estimate and the uniform blow-up estimate for the blow-up solution.     

Properties of non-simultaneous blow-up solutions in nonlocal parabolic equations

This paper deals with blow-up solutions in parabolic equations coupled via nonlocal nonlinearities, subject to homogeneous Dirichlet conditions. Firstly, some criteria on non-simultaneous and simultaneous blow-up are given, including four kinds of phenomena: (i) the existence of non-simultaneous blow-up; (ii) the coexistence of non-simultaneous and simultaneous blow-up; (iii) any blow-up must be simultaneous; (iv) any blow-up must be non-simultaneous. Next, total versus single point blow-up are classified completely. Moreover, blow-up rates are obtained for both non-simultaneous and simultaneous blow-up solutions.     

Roles of weight functions to a nonlinear porous medium equation with nonlocal source and nonlocal boundary condition

In this paper we investigates the blow-up properties of the positive solutions to a porous medium equation with nonlocal reaction source and with nonlocal boundary condition, we obtain the blow-up condition and its blow-up rate estimate.     

GLOBAL BLOW-UP FOR A DEGENERATE AND SINGULAR NONLOCAL PARABOLIC EQUATION WITH WEIGHTED NONLOCAL BOUNDARY CONDITIONS

This paper deals with the blow-up properties of positive solutions to a degenerate and singular nonlocal parabolic equation with weighted nonlocal boundary conditions.Under appropriate hypotheses, the global existence and finite time blow-up of positive solutions are obtained. Furthermore, by using the properties of Green's function, we find that the blow-up set of the blow-up solution is the whole domain(0, a), and this differs from parabolic equations with local sources case.     

A degenerate parabolic system with nonlocal boundary condition

In this article, we investigate the blow-up properties of the positive solutions to a degenerate parabolic system with nonlocal boundary condition. We give the criteria for finite time blow-up or global existence, which shows the important influence of nonlocal boundary. And then we establish the precise blow-up rate estimate for small weighted nonlocal boundary.     

A Quasilinear Parabolic System with Nonlocal Boundary Conditions and Localized Sources

This paper investigates the properties of solutions to a quasilinear parabolic system with nonlocal boundary conditions and localized sources. Conditions for the existence of global or blow-up solutions are given. Global blow-up property and blow-up rate estimates are also derived.     

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.     

Evolutions of the momentum density,deformation tensor and the nonlocal term of the Camassa–Holm equation

Methods originally developed to study the finite time blow-up problem of the regular solutions of the three dimensional incompressible Euler equations are used to investigate the regular solutions of the Camassa–Holm equation. We obtain results on the relative behaviors of the momentum density, the deformation tensor and the nonlocal term along the trajectories. In terms of these behaviors, we get new types of asymptotic properties of global solutions, blow-up criterion and blow-up time estimate for local solutions. More precisely, certain ratios of the quantities are shown to be vaguely monotonic along the trajectories of global solutions. Finite time blow-up of the accumulated momentum density is necessary and sufficient for the finite time blow-up of the solution. An upper estimate of the blow-up time and a blow-up criterion are given in terms of the initial short time trajectorial behaviors of the deformation tensor and the nonlocal term.