JournalsjemsVol. 17, No. 9pp. 2103–2135

Stability properties for quasilinear parabolic equations with measure data

  • Marie-Françoise Bidaut-Véron

    Université de Tours, France
  • Quoc-Hung Nguyen

    Université de Tours, France
Stability properties for quasilinear parabolic equations with measure data cover
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Abstract

Let Ω\Omega be a bounded domain of RN\mathbb{R}^{N}, and Q=Ω×(0,T).Q=\Omega \times(0,T). We study problems of the model type

\left\{ \begin{array} [c]{l}% {u_{t}}-{\Delta_{p}}u=\mu\qquad\text{in }Q,\\ {u}=0\qquad\text{on }\partial\Omega\times(0,T),\\ u(0)=u_{0}\qquad\text{in }\Omega, \end{array} \right.

where p>1p>1, μMb(Q)\mu\in\mathcal{M}_{b}(Q) and u0L1(Ω).u_{0}\in L^{1}(\Omega). Our main result is a \textit{stability theorem }extending the results of Dal Maso, Murat, Orsina, Prignet, for the elliptic case, valid for quasilinear operators uA(u)=u\longmapsto\mathcal{A}(u)=div(A(x,t,u))(A(x,t,\nabla u)).

Cite this article

Marie-Françoise Bidaut-Véron, Quoc-Hung Nguyen, Stability properties for quasilinear parabolic equations with measure data. J. Eur. Math. Soc. 17 (2015), no. 9, pp. 2103–2135

DOI 10.4171/JEMS/552