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This paper concerns with existence, uniqueness and asymptotic behavior of the solutions for a nonlocal coupled system of reaction-diffusion. We prove the existence and uniqueness of weak solutions by the Faedo-Galerkin method and exponential decay of solutions by the classic energy method. We improve the results obtained by Chipot-Lovato and Menezes for… (More)
In this paper we establish the existence and uniqueness of global classical solutions for the equation which arises in the study of the extensional vibrations of thin rod, or torsional vibrations of thin rod.
In this paper we consider the nonlinear degenerate evolution equation with strong damping, in Q-x]O,T[ *) u(x,O)-uo,(Ku’)(x,O)-O in [ufx, t)0 on --r, where K is a function with K(x, t) > O, K(x, O) 0 and F is a continuous real function satisfying (**) sF(s) O, for all s E R, f is a bounded domain of R", with smooth boundary I". We prove the existence of a… (More)
In this work we consider the Von Kármán system with frictional damping acting on the displacement and using the Method of Nakao we prove the exponential decay of the solution. The numerical scheme is presented for calculate the solution and to verify the long-time decay energy.
In this paper, we investigate a mathematical model for a nonlinear coupled system of Kirchhoff type of beam equations with nonlocal boundary conditions. We establish existence, regularity and uniqueness of strong solutions. Furthermore, we prove the uniform rate of exponential decay. The uniform rate of polynomial decay is considered. 2000 Mathematical… (More)