带非局部边界条件的半线性抛物系统的一致爆破模式

文章主要讨论一类带有非局部源与边界条件的半线性抛物系统,通过使用上解与下解技术,证明了系统整体解的存在与有限时间爆破的结果, 而且,还得到了解的一致爆破模式.     

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.     

具非局部源退化抛物型方程组的一致爆破模式

考虑带有齐次Dirichlet边界条件且具有非局部源项的退化抛物型方程组正解的爆破性质. 在适当条件下, 建立了该问题解的局部存在性并证明解在有限时刻爆破, 此外,还导出了解的两个分量同时爆破的必要条件, 并得到了该问题解的一致爆破模式.     

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.     

一类反应扩散系统的不同时爆破临界指标(英文)

本文讨论了一类反应扩散方程组齐次第一初边值问题u_t=△u+u~mv~p,v_t=△v+u~qv~n的不同时爆破临界指标问题.在一定初值条件下,本文给出了径向解的四种同时、不同时爆破现象:存在初值使得同时爆破或不同时爆破发生;任何爆破均是同时或不同时的.通过对指标参数的完整分类给出了四种爆破现象的充分必要条件,并且得到了解的全部爆破速率估计.所得结果推广了以前的相应工作.     

有非局部源退化抛物方程组解的爆破

本文讨论一类具有非局部源退化抛物方程组．通过利用上下解方法得到解的全局存在和有限时刻爆破，给出爆破集是整个区域，而且得到了解的爆破率．     

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     

R~2中具有趋化性的抛物-椭圆系统的解的性态分析

在二维空间中讨论了一个抛物-椭圆系统,而该系统来源于生物学中的趋化性模型.主要在Sobolev空间的框架下讨论了解的全局存在性与解的爆破性质,得出结论该系统存在一个门槛值,而该值决定了解全局存在或者发生爆破.最后利用利李亚普诺夫函数给出了定理的证明并得出结论.     

具非局部源反应扩散方程组解的同时爆破与不同时爆破

本文讨论具齐次Dirichlet边界条件非局部源反应扩散方程组的爆破解,给出四类同时爆破与不同时爆破现象的判定指标,这四类爆破现象包含:(i)存在不同时爆破;(ii)同时爆破与不同时爆破共存;(iii)任意爆破必是同时爆破;(iv)任意爆破必是不同时爆破.     

Blow-up for a degenerate reaction-diffusion system with nonlinear localized sources

This paper deals with the global existence and blow-up of nonnegative solution of the degenerate reaction-diffusion system with nonlinear localized sources involved a product with local terms. We investigate the influence of localized sources and local terms on global existence and blow up for this system. Moreover, we establish the precise blow-up estimates. Finally, for the special case p₁=p₂=0, we show the blow-up set is whole region and the uniform blow-up profiles are obtained. These extend a resent work of Chen and Xie in [Y. Chen, C. Xie, Blow-up for a porous medium equation with a localized source, Appl. Math. Comput. 159 (2004) 79-93], which considered the single equation with localized sources.     

Global weak solutions and blow-up structure for the Degasperis-Procesi equation

In this paper we study several qualitative properties of the Degasperis-Procesi equation. We first established the precise blow-up rate and then determine the blow-up set of blow-up strong solutions to this equation for a large class of initial data. We finally prove the existence and uniqueness of global weak solutions to the equation provided the initial data satisfies appropriate conditions.     

一类带非局部源项的p-Laplace方程解的整体存在与爆破

本文研究一类在Neumann边值条件下带局部源项的p-Laplace方程解的整体存在和爆破性.利用微分不等式技巧,通过构造辅助函数的方法,获得了方程的解整体存在和解在有限时间爆破的充分条件,以及爆破时间的上下界估计,推广了相关文献结论.     

Global existence and blow-up of solutions of nonlocal diffusion problems with free boundaries

In this paper, we investigate some nonlocal diffusion problems with free boundaries. We first give the existence and uniqueness of local solution by the ODE basic theory and the contraction mapping principle. Then we provide a complete classification for the global existence and finite time blow-up of solutions. Moreover, estimates of blow-up rate and blow-up time are also obtained for the blow-up solution.     

Blow-up for the Timoshenko-type equation with variable exponents

The finite time blow-up of solutions to a nonlinear Timoshenko-type equation with variable exponents is studied. More concretely, we prove that the solutions blow up in finite time with positive initial energy. Also, the existence of finite time blow-up solutions with arbitrarily high initial energy is established. Meanwhile, the upper and lower bounds of the blow-up time are derived. These results deepen and generalize the ones obtained in [Nonlinear Anal. Real World Appl., 61: Paper No. 103341, 2021].     

Existence and Blow-Up Behavior for Solutions of the Generalized Jang Equation

The generalized Jang equation was introduced in an attempt to prove the Penrose inequality in the setting of general initial data for the Einstein equations. In this paper we give an extensive study of this equation, proving existence, regularity, and blow-up results. In particular, precise asymptotics for the blow-up behavior are given, and it is shown that blow-up solutions are not unique.     

The Cauchy problem for the dissipative Boussinesq equation

This work is devoted to the solvability and finite time blow-up of solutions of the Cauchy problem for the dissipative Boussinesq equation in all space dimension. We prove the existence and uniqueness of local mild solutions in the phase space by means of the contraction mapping principle. By establishing the time-space estimates of the corresponding Green operators, we obtain the continuation principle. Under some restriction on the initial data, we further study the results on existence and uniqueness of global solutions and finite time blow-up of solutions with the initial energy at three different level. Moreover, the sufficient and necessary conditions of finite time blow-up of solutions are given.     

Existence, non-existence and asymptotic behavior of blow-up entire solutions of semilinear elliptic equations

We are mainly concerned with existence, non-existence and the behavior at infinity of non-negative blow-up entire solutions of the equation Δu=ρ(x)f(u) in RN. No monotonicity condition is assumed upon f and, in fact, we obtain solutions with a prescribed behavior both at infinity and at the origin. The method used to get existence is based upon lower and upper solutions techniques while for non-existence we explore radial symmetry, estimates on an associated integral equation and the Keller-Osserman condition.     

Blow-up for Strauss type wave equation with damping and potential

We study a kind of nonlinear wave equations with damping and potential, whose coefficients are both critical in the sense of the scaling and depend only on the spatial variables. Based on the earlier works, one may think there are two kinds of blow-up phenomenons when the exponent of the nonlinear term is small. It also means there are two kinds of law to determine the critical exponent. In this paper, we obtain a blow-up result and get the estimate of the upper bound of the lifespan in critical and sub-critical cases. All of the results support such a conjecture, although for now, the existence part is still open.     

Nonlinear Degenerate Parabolic Equation with Nonlinear Boundary Condition

In this paper, we obtain the necessary and sufficient conditions on the global existence of all positive （weak） solutions to a nonlinear degenerate parabolic equation with nonlinear boundary condition.