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فهرست مقالات

Global attractor for a nonlocal hyperbolic problem on {mathcal{R}}^{N}


علمی-پژوهشی (وزارت علوم)/ISC (10 صفحه - از 159 تا 168)


We consider the quasilinear Kirchhoff's problem u_{tt}-phi (x)||nabla u(t)||^{2}Delta u+f(u)=0 ,;; x in {mathcal{R}}^{N}, ;; t geq 0,with the initial conditions u(x,0) = u_0 (x) and u_t(x,0) = u_1 (x), in the case where N geq 3, ; f(u)=|u|^{a}u and (phi (x))^{-1} in L^{N/2}({mathcal{R}}^{N})cap L^{infty}({mathcal{R}}^{N} ) is a positive function. The purpose of our work is to study the long time behaviour of the solution of this equation. Here, we prove the existence of a global attractor for this equation in the strong topology of the space {cal X}_{1}=:{cal D}^{1,2}({mathcal{R}}^{N}) times L^{2}_{g}({mathcal{R}}^{N}). We succeed to extend some of our earlier results concerning the asymptotic behaviour of the solution of the problem.

کلیدواژه ها:

quasilinear hyperbolic equations ،Kirchhoff strings ،global attractor ،generalised Sobolev spaces ،weighted L^p Spaces

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