Parabolic equations with exponential nonlinearity and measure data

Abstract

Let $\Omega$ be a bounded domain in ${\mathbb{R}}^N$ and $T>0$. We study the problem \begin{equation} (P)\left\{ \begin{array}{lll} u_t - Δu \pm g(u) &= μ\quad &\text{in } Q_T:=Ω\times (0,T) \\ \phantom{------,} u&=0 &\text{on } \partial Ω\times (0,T)\\ \phantom{----,} u(.,0) &=ω&\text{in } Ω. \end{array} \right. \end{equation} where $\mu$ and $\omega$ are bounded Radon measures in $Q_T$ and $\Omega$ respectively and $g(u)\sim e^{a|u{|}^q}$ with $a>0$ and $q\ge 1$. We provide a sufficient condition in terms of fractional maximal potentials of $\mu$ and $\omega$ for solving (P).

22 pages

References in corpus (1)

• Stability properties for quasilinear parabolic equations with measure data and applications

Cited by in corpus (1)

• Wiener criteria for existence of large solutions of nonlinear parabolic equations with absorption in a non-cylindrical domain