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Article Dans Une Revue Communications in Contemporary Mathematics Année : 2014

Evolution equations of p-Laplace type with absorption or source terms and measure data

Résumé

Let $\Omega$ be a bounded domain of $\mathbb{R}^{N}$, and $Q=\Omega \times(0,T).$ We consider problems\textit{ }of the type % \[ \left\{ \begin{array} [c]{l}% {u_{t}}-{\Delta_{p}}u\pm\mathcal{G}(u)=\mu\qquad\text{in }Q,\\ {u}=0\qquad\text{on }\partial\Omega\times(0,T),\\ u(0)=u_{0}\qquad\text{in }\Omega, \end{array} \right. \] where ${\Delta_{p}}$ is the $p$-Laplacian, $\mu$ is a bounded Radon measure, $u_{0}\in L^{1}(\Omega),$ and $\pm\mathcal{G}(u)$ is an absorption or a source term$.$ In the model case $\mathcal{G}(u)=\pm\left\vert u\right\vert ^{q-1}u$ $(q>p-1),$ or $\mathcal{G}$ has an exponential type. We prove the existence of renormalized solutions for any measure $\mu$ in the subcritical case, and give sufficient conditions for existence in the general case, when $\mu$ is good in time and satisfies suitable capacitary conditions.
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Dates et versions

hal-01060687 , version 1 (04-09-2014)

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Marie-Françoise Bidaut-Véron, Quoc-Hung Nguyen. Evolution equations of p-Laplace type with absorption or source terms and measure data. Communications in Contemporary Mathematics, 2014, ⟨10.1142/S0219199715500066⟩. ⟨hal-01060687⟩
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