共查询到20条相似文献,搜索用时 15 毫秒
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Weibing Deng Yuxiang Li Chunhong Xie 《Proceedings of the American Mathematical Society》2003,131(5):1573-1582
This paper establishes a new criterion for global existence and nonexistence of positive solutions of the non-local degenerate parabolic system
0, \end{align*}">
with homogeneous Dirichlet boundary conditions, where is a bounded domain with a smooth boundary and are positive constants. For all initial data, it is proved that there exists a global positive solution iff , where is the unique positive solution of the linear elliptic problem
0, \end{align*}">
with homogeneous Dirichlet boundary conditions, where is a bounded domain with a smooth boundary and are positive constants. For all initial data, it is proved that there exists a global positive solution iff , where is the unique positive solution of the linear elliptic problem
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The initial and boundary value problem for the degenerate parabolic equation vt = Δ(?(v)) + F(v) in the cylinder bounded, for a certain class of point functions ? satisfying ?′(v) ? 0 (e.g., ) is considered. In the case that F(v) sign , the equation has a global time solution. The same is true for α = 1 provided the measure of Ω is sufficiently small. In the case that is nondecreasing a condition is given on the initial state v(x, 0) which implies that the solution must blow up in finite time. The existence of such initial states is discussed. 相似文献
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We consider the Cauchy problem for a doubly nonlinear degenerate parabolic equation with nonlocal source under the assumption
that the initial function is integrable. We establish the existence and nonexistence of time-global solutions of the problem.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 11, pp. 1443–1464, November, 2005. 相似文献
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We study local and global existence of solutions for some semilinear parabolic initial boundary value problems with autonomous nonlinearities having a “Newtonian” nonlocal term. 相似文献
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Existence of solutions for degenerate quasilinear parabolic equations of higher order 总被引:2,自引:0,他引:2
Liu Zhenhai 《数学学报(英文版)》1997,13(4):465-472
In the paper, existence results for degenerate parabolic boundary value problems of higher order are proved. The weak solution
is sought in a suitable weighted Sobolev space by using the generalized degree theory.
Supported by the funds of the State Educational Commission of China for returned scholars from abroad. 相似文献
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In this paper, we prove the existence of Fujita-type critical exponents for x-dependent fully nonlinear uniformly parabolic equations of the type $$(*)\quad \partial_{t}u=F(D^{2}u,x)+u^{p}\quad{\rm in}\ \ \mathbb{R}^{N}\times\mathbb{R}^{+}.$$ These exponents, which we denote by p(F), determine two intervals for the p values: in ]1,p(F)[, the positive solutions have finite-time blow-up, and in ]p(F), +∞[, global solutions exist. The exponent p(F)?=?1?+?1/α(F) is characterized by the long-time behavior of the solutions of the equation without reaction terms $$\partial_{t}u=F(D^{2}u,x)\quad{\rm in}\ \ \mathbb{R}^{N}\times\mathbb{R}^{+}.$$ When F is a x-independent operator and p is the critical exponent, that is, p?=?p(F). We prove as main result of this paper that any non-negative solution to (*) has finite-time blow-up. With this more delicate critical situation together with the results of Meneses and Quaas (J Math Anal Appl 376:514–527, 2011), we completely extend the classical result for the semi-linear problem. 相似文献
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Youpeng Chen Qilin Liu Chunhong Xie 《Proceedings of the American Mathematical Society》2004,132(1):135-145
This paper deals with the blow-up properties of the solution to the degenerate nonlinear reaction diffusion equation with nonlocal source in subject to the homogeneous Dirichlet boundary conditions. The existence of a unique classical nonnegative solution is established and the sufficient conditions for the solution exists globally or blows up in finite time are obtained. Furthermore, it is proved that under certain conditions the blow-up set of the solution is the whole domain.
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Shaohua Chen 《Journal of Differential Equations》2008,245(4):1112-1136
The author discusses the degenerate and quasilinear parabolic system
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Impulsive effects on global existence of solutions for degenerate semilinear parabolic equations 总被引:4,自引:0,他引:4
Let q be a nonnegative real number, and λ and σ be positive constants. This article studies the following impulsive problem: for n = 1, 2, 3,…, . The number λ* is called the critical value if the problem has a unique global solution u for λ < λ*, and the solution blows up in a finite time for λ > λ*. For σ < 1, existence of a unique λ* is established, and a criterion for the solution to decay to zero is studied. For σ > 1, existence of a unique λ* and three criteria for the blow-up of the solution in a finite time are given respectively. It is also shown that there exists a unique T* such that u exists globally for T> T*, and u blows up in a finite time for T < T*. 相似文献