Some noncoercive parabolic equations with lower order terms in divergence form

Lucio Boccardo, Luigi Orsina and Alessio Porretta
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Lucio Boccardo: Università di Roma 1, Dipartimento di Matematica
Luigi Orsina: Università di Roma “La Sapienza”, Dipartimento di Matematica
Alessio Porretta: Università di Roma “Tor Vergata”, Dipartimento di Matematica

A chapter in Nonlinear Evolution Equations and Related Topics, 2003, pp 407-418 from Springer

Abstract: Abstract This paper deals with existence and regularity results for the problem $$ \left\{ \begin{gathered} {u_{t}} - {\text{div}}(a(x,t,u)\nabla u) = - {\text{div}}(u{\text{E}}), in \Omega x{\text{ }}(0,T), \hfill \\ u = 0 on \partial \Omega x (0,T), \hfill \\ u(0) = {u_{0}} in \Omega , \hfill \\ \end{gathered} \right. $$ , under various assumptions on E and u 0. The main difficulty in studying this problem is due to the presence of the term div(uE), which makes the differential operator non coercive on the “energy space” L2(0T; H 0 1 (Ω)).

Keywords: 35K10; 35K15; 35K65; Nonlinear parabolic equations; noncoercive problems; infinite energy solutions (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-7924-8_22

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DOI: 10.1007/978-3-0348-7924-8_22

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