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Article type: Research Article
Authors: Leonori, Tommaso | Petitta, Francesco
Affiliations: Dipartimento di Matematica, Università di Tor Vergata, Via della ricerca scientifica 1, 00133, Roma, Italy E-mail: leonori@mat.uniroma2.it | Dipartimento di Matematica, Università La Sapienza, Piazzale A. Moro 2, 00185, Roma, Italy E-mail: petitta@mat.uniroma1.it
Abstract: In this paper we deal with the asymptotic behavior of solution for quasilinear parabolic equations with absorbing lower-order terms whose model is \[\cases{u_{t}-\Delta u+u|\nabla u|^{2}=f& \mbox{in} \varOmega \times(0,T),\cr\noalign{\vspace{3pt}}u(x,0)=u_{0}& \mbox{in} \varOmega ,}\] with L1 data that do not depend on time. The main result states that, under suitable assumptions, the solution of the parabolic problem converges to the stationary solution.
Keywords: asymptotic behavior, quasilinear parabolic equations, natural growth
Journal: Asymptotic Analysis, vol. 48, no. 3, pp. 219-233, 2006
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