Asymptotic behavior for solutions of parabolic equations with natural growth terms and irregular data

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: [email protected] | Dipartimento di Matematica, Università La Sapienza, Piazzale A. Moro 2, 00185, Roma, Italy E-mail: [email protected]

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