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1.
Finite time blow-up and global existence of weak solutions for pseudo-parabolic equation with exponential nonlinearity 下载免费PDF全文
This paper is concerned with the initial boundary value problem of a class of pseudo-parabolic equation $u_t - \triangle u - \triangle u_t + u = f(u)$ with an exponential nonlinearity. The eigenfunction method and the Galerkin method are used to prove the blow-up, the local existence and the global existence of weak solutions. Moreover, we also obtain other properties of weak solutions by the eigenfunction method. 相似文献
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This article deals with the conditions that ensure the blow-up phenomenon or its absence for solutions of the system ut=△ul up1vq1 and vt=△vm up2vq2 with homogeneous Dirichlet boundary conditions. The results depend crucially on the sign of the difference p2q1-(l-P1)(m-q2), the initial data, and the domainΩ. 相似文献
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We present results for finite time blow-up for filtration problems with nonlinear reaction under appropriate assumptions on the nonlinearities and the initial data. In particular, we prove first finite time blow-up of solutions subject to sufficiently large initial data provided that the reaction term “overpowers” the nonlinear diffusion in a certain sense. Secondly, under related assumptions on the nonlinearities, we show that initial data above positive stationary state solutions will always lead to finite time blow-up. 相似文献
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Yaojun Ye 《Applicable analysis》2017,96(16):2869-2890
The initial-boundary value problem for a system of Petrovsky equations with memory and nonlinear source terms in bounded domain is studied. The existence of global solutions for this problem is proved by constructing a stable set, and obtain the exponential decay estimate of global solutions. Meanwhile, under suitable conditions on relaxation functions and the positive initial energy as well as non-positive initial energy, it is proved that the solutions blow up in the finite time and the lifespan estimates of solutions are also given. 相似文献
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Abstract By exploring a local geometric property of the vorticity field along a vortex filament, we establish a sharp relationship between the geometric properties of the vorticity field and the maximum vortex stretching. This new understanding leads to an improved result of the global existence of the 3D Euler equation under mild assumptions. 相似文献
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Global analysis of the shadow Gierer-Meinhardt system with general linear boundary conditions in a random environment 下载免费PDF全文
Kwadwo Antwi-Fordjour Seonguk Kim Marius Nkashama 《Journal of Applied Analysis & Computation》2020,10(5):1980-1994
The global analysis of the shadow Gierer-Meinhardt system with multiplicative white noise and general linear boundary conditions is investigated in this paper.
For this reaction-diffusion system, we employ a fixed point argument to prove local existence and uniqueness. Our results on global existence are based on \emph{a priori} estimates of solutions. 相似文献
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This paper deals with a class of porous medium systems with moving localized sources ut=ur1(Δu+af(v(x0(t),t))),vt=vr2(Δv+bg(u(x0(t),t))) with homogeneous Dirichlet boundary conditions. It is shown that under certain conditions, solutions of the above system blow up in finite time for large a and b or large initial data while there exist global positive solutions to the above system for small a and b or small initial data. Moreover, in the one dimensional space case, it is also shown that all global positive solutions of the above problem are uniformly bounded. 相似文献
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Yasuhito Miyamoto 《Journal of Differential Equations》2006,223(1):185-207
We are concerned with the following Gierer-Meinhardt model on a bounded domain with smooth boundary ∂Ω which is a biological pattern formation model proposed by A. Gierer and H. Meinhardt
(GM) 相似文献
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We study a type of nonlinear parabolic equations. In terms of the variational characterization of the corresponding nonlinear elliptic equations and the invariant flow arguments, we establish the sharp criteria for global existence and blow-up. Furthermore, we also get the instability of the steady states and the global existence with small initial data. 相似文献
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A parabolic–elliptic Keller–Segel system with homogeneous Neumann boundary condition is considered in a radially symmetric domain where and is a -dimensional ball of radius We assert that under a condition on the initial data, radial weak solutions blow-up in finite time when 相似文献
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In this paper a porous medium equation with a moving localized source ut=ur(Δu+af(u(x0(t),t))) is considered. It is shown that under certain conditions solutions of the above equation blow up in finite time for large a or large initial data while there exist global positive solutions to the above equation for small a or small initial data. Moreover, in one space dimension case, it is also shown that all global positive solutions of the above equation are uniformly bounded, and this differs from that of a porous medium equation with a local source. 相似文献
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Global existence to generalized Boussinesq equation with combined power-type nonlinearities 总被引:1,自引:0,他引:1
The Cauchy problem to the generalized Boussinesq equation with combined power-type nonlinearities is studied. Global solvability or finite time blow-up of the solutions with subcritical initial energy is proved by means of the sign preserving property of the Nehari functional. For generalized Lienard (or generalized Bernoulli) nonlinear terms the critical energy constant is explicitly evaluated. A new method, that can be considered as a modification of the potential well method, is developed. The performed numerical experiments support the theoretical results. 相似文献
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Ross G. Pinsky 《Proceedings of the American Mathematical Society》1999,127(11):3319-3327
We consider the inhomogeneous equation
where , and , and give criteria on , and which determine whether for all and all the solution blows up in finite time or whether for and sufficiently small, the solution exists for all time.
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This paper deals with p-Laplacian systemswith null Dirichlet boundary conditions in a smooth bounded domain ΩRN, where p,q>1, , and a,b>0 are positive constants. We first get the non-existence result for a related elliptic systems of non-increasing positive solutions. Secondly by using this non-existence result, blow-up estimates for above p-Laplacian systems with the homogeneous Dirichlet boundary value conditions are obtained under Ω=BR={xRN:|x|<R}(R>0). Then under appropriate hypotheses, we establish local theory of the solutions and obtain that the solutions either exists globally or blow-up in finite time. 相似文献
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Yuxiang Li Weibing Deng Chunhong Xie 《Proceedings of the American Mathematical Society》2002,130(12):3661-3670
The initial-boundary value problems are considered for the strongly coupled degenerate parabolic system
in the cylinder , where is bounded and are positive constants. We are concerned with the global existence and nonexistence of the positive solutions. Denote by the first Dirichlet eigenvalue for the Laplacian on . We prove that there exists a global solution iff .
in the cylinder , where is bounded and are positive constants. We are concerned with the global existence and nonexistence of the positive solutions. Denote by the first Dirichlet eigenvalue for the Laplacian on . We prove that there exists a global solution iff .
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In this paper we study the initial boundary value problem of a class of semilinear parabolic equation. Our main tools are the comparison principle and variational methods. In this paper, we will find both finite time blow-up and global solutions at high energy level. 相似文献