共查询到20条相似文献,搜索用时 15 毫秒
1.
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. 相似文献
2.
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. 相似文献
3.
Bingchen Liu 《Applicable analysis》2013,92(10):1615-1627
This article deals with blow-up solutions in reaction–diffusion equations coupled via localized exponential sources, subject to null Dirichlet conditions. The optimal and complete classification is obtained for simultaneous and non-simultaneous blow-up solutions. Moreover, blow-up rates and blow-up sets are also discussed. It is interesting that, in some exponent regions, blow-up phenomena depend sensitively on the choosing of initial data, and the localized nonlinearities play important roles in the blow-up properties of solutions. 相似文献
4.
This article deals with a class of nonlocal and degenerate quasilinear parabolic equation u t = f(u)(Δu + a∫Ω u(x, t)dx ? u) with homogeneous Dirichlet boundary conditions. The local existence of positive classical solutions is proved by using the method of regularization. The global existence of positive solutions and blow-up criteria are also obtained. Furthermore, it is shown that, under certain conditions, the solutions have global blow-up property. When f(s) = s p , 0 < p ≤ 1, the blow-up rate estimates are also obtained. 相似文献
5.
In this article, a porous medium equation with nonlocal boundary condition and a localized source is studied. The results of the existence of global solutions or blow-up of solutions are given. The blow-up rate estimates are also obtained under some conditions. 相似文献
6.
《数学季刊》2016,(2):125-138
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. 相似文献
7.
We study blow-up, global existence and ground state solutions for the N-coupled focusing nonlinear SchrSdinger equations. Firstly, using the Nehari manifold approach and some variational techniques, the existence of ground state solutions to the equations (CNLS) is established. Secondly, under certain conditions, finite time blow-up phenomena of the solutions is derived. Finally, by introducing a refined version of compactness lemma, the L2 concentration for the blow-up solutions is obtained. 相似文献
8.
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. 相似文献
9.
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. 相似文献
10.
Using the upper and lower solution techniques and Hopf's maximum principle, the sufficient conditions for the existence of blow-up positive solution and global positive solution are obtained for a class of quasilinear parabolic equations subject to Neumann boundary conditions. An upper bound for the ‘blow-up time’, an upper estimate of the ‘blow-up rate’, and an upper estimate of the global solution are also specified. 相似文献
11.
Qiaoyi Hu 《Applicable analysis》2013,92(2):398-410
We study the Cauchy problem of a weakly dissipative 2-component Camassa–Holm system. We first establish local well-posedness for a weakly dissipative 2-component Camassa–Holm system. We then present a global existence result for strong solutions to the system. We finally obtain several blow-up results and the blow-up rate of strong solutions to the system. 相似文献
12.
Qilin Liu Yuxiang Li Hongjun Gao 《Journal of Mathematical Analysis and Applications》2006,320(2):771-778
In this short paper, we investigate blow-up rate of solutions of reaction–diffusion equations with localized reactions. We prove that the solutions have a global blow-up and the rate of blow-up is uniform in all compact subsets of the domain. 相似文献
13.
The initial-boundary value problem for semilinear wave equation systems with a strong dissipative term in bounded domain is studied. The existence of global solutions for this problem is proved by using potential well method, and the exponential decay of global solutions is given through introducing an appropriate Lyapunov function. Meanwhile, blow-up of solutions in the unstable set is also obtained. 相似文献
14.
Hui-ling LI & Ming-xin WANG Department of Mathematics Southeast University Nanjing China 《中国科学A辑(英文版)》2007,50(4):590-608
This paper deals with the properties of positive solutions to a quasilinear parabolic equation with the nonlinear absorption and the boundary flux. The necessary and sufficient conditions on the global existence of solutions are described in terms of different parameters appearing in this problem. Moreover, by a result of Chasseign and Vazquez and the comparison principle, we deduce that the blow-up occurs only on the boundary (?)Ω. In addition, for a bounded Lipschitz domainΩ, we establish the blow-up rate estimates for the positive solution to this problem with a= 0. 相似文献
15.
In this article, we consider a two-component nonlinear shallow water system, which includes the famous 2-component Camassa-Holm and Degasperis-Procesi equations as special cases. The local well-posedess for this equations is established. Some sufficient conditions for blow-up of the solutions in finite time are given. Moreover, by separation method, the self-similar solutions for the nonlinear shallow water equations are obtained, and which local or global behavior can be determined by the corresponding Emden equation. 相似文献
16.
Ardak Kashkynbayev Durvudkhan Suragan Berikbol T. Torebek 《Mathematische Nachrichten》2023,296(6):2395-2403
In this paper, we consider the Fisher–KPP equation on the Heisenberg group. We discuss the existence of global solutions, asymptotic behavior of global solutions and blow-up solutions. Moreover, we extend the obtained results to the time-fractional Fisher–KPP equation on the Heisenberg group. 相似文献
17.
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. 相似文献
18.
This paper is concerned with the blow-up solutions of the Cauchy problem for Gross-Pitaevskii equation.In terms of Merle and Raphёel's arguments as well as Carles' transformation,the limiting profiles of blow-up solutions are obtained.In addition,the nonexistence of a strong limit at the blow-up time and the existence of L2 profile outside the blow-up point for the blow-up solutions are obtained. 相似文献
19.
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. 相似文献