共查询到20条相似文献,搜索用时 15 毫秒
1.
Blow-up of positive-initial-energy solutions of a nonlinear viscoelastic hyperbolic equation 总被引:2,自引:0,他引:2
Salim A. Messaoudi 《Journal of Mathematical Analysis and Applications》2006,320(2):902-915
In this paper, we consider the nonlinear viscoelastic equation with initial conditions and Dirichlet boundary conditions. For nonincreasing positive functions g and for p>m, we prove that there are solutions with positive initial energy that blow up in finite time. 相似文献
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In this paper we consider a system of nonlinear viscoelastic wave equations. Under arbitrary positive initial energy and standard conditions on the relaxation functions, we prove a finite-time blow-up result. 相似文献
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In this paper, we consider a strongly damped wave equation with fractional damping on part of its boundary and also with an internal source. Under some appropriate assumptions on the parameters, and with certain initial data, a blow-up result with positive initial energy is established. 相似文献
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Howard A. Levine Grozdena Todorova 《Proceedings of the American Mathematical Society》2001,129(3):793-805
In this paper we consider the long time behavior of solutions of the initial value problem for semi-linear wave equations of the form
Here 0.$">
We prove that if m \ge 1,$"> then for any 0$"> there are choices of initial data from the energy space with initial energy such that the solution blows up in finite time. If we replace by , where is a sufficiently slowly decreasing function, an analogous result holds.
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This article is concerned with a class of semilinear parabolic equations with variable reaction with homogeneous Dirichlet boundary conditions. Under some appropriate assumptions on the parameters, and with certain initial data, a blow-up result is established with positive initial energy. 相似文献
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In this work we consider a Cauchy problem for a nonlinear viscoelastic equation. Under suitable conditions on the initial data and the relaxation function, we prove a finite-time blow-up result. 相似文献
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Semilinear hyperbolic and parabolic initial–boundary value problems are studied. Criteria for solutions of a semilinear hyperbolic equation and a parabolic equation with general forcing term and general boundary condition to blow up in finite time are obtained. 相似文献
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Global existence and blow-up of solutions for a system of nonlinear viscoelastic wave equations with damping and source 总被引:1,自引:0,他引:1
In this paper we investigate the global existence and finite time blow-up of solutions to the system of nonlinear viscoelastic wave equations in Ω×(0,T) with initial and Dirichlet boundary conditions, where Ω is a bounded domain in . Under suitable assumptions on the functions gi(), , the initial data and the parameters in the equations, we establish several results concerning local existence, global existence, uniqueness and finite time blow-up property. 相似文献
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In this study, we consider a class of wave equations with strong damping and source terms associated with initial and Dirichlet boundary conditions. We establish a blow up result for certain solutions with nonpositive initial energy as well as positive initial energy. This further improves the results by Yang (Math. Meth. Appl. Sci. 2002; 25 :825–833) and Messaudi and Houari (Math. Meth. Appl. Sci. 2004; 27 : 1687–1696). Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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In this paper we consider the nonlinear viscoelastic equation
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Kazuhiro Ishige 《Journal of Differential Equations》2005,212(1):114-128
We consider the blow-up problem of a semilinear heat equation,
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Salim A. Messaoudi 《Journal of Mathematical Analysis and Applications》2008,341(2):1457-1467
In this paper we consider the following viscoelastic equation:
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This paper presents the exponential stability of a one-dimensional wave equation with viscoelastic damping. Using the asymptotic analysis technique, we prove that the spectrum of the system operator consists of two parts: the point and continuous spectrum. The continuous spectrum is a set of N points which are the limits of the eigenvalues of the system, and the point spectrum is a set of three classes of eigenvalues: one is a subset of N isolated simple points, the second is approaching to a vertical line which parallels to the imagine axis, and the third class is distributed around the continuous spectrum. Moreover, the Riesz basis property of the generalized eigenfunctions of the system is verified. Consequently, the spectrum-determined growth condition holds true and the exponential stability of the system is then established. 相似文献
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In this paper, the existence and uniqueness of the local generalized solution and the local classical solution for the initial boundary value problem of the quasi-linear wave equation with viscous damping are proved. The nonexistence of the global solution for this problem is discussed by an ordinary differential inequality. Finally, an example is given. 相似文献
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Hongyinping Feng Shengjia Li 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(4):2273-2280
In this paper we consider the wave equation with nonlinear damping and source terms. We are interested in the interaction between the boundary damping −|yt(L,t)|m−1yt(L,t) and the interior source |y(t)|p−1y(t). We find a sufficient condition for obtaining the blow-up solution of the problem. Furthermore, we also obtain that the solution may blow up even if m≥p. 相似文献