Parabolic equations with exponential nonlinearity and measure data
Phuoc‐Tai Nguyen · arXiv (Cornell University) · 2013
Let $Ω$ 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 $μ$ and $ω$ are bounded Radon measures in $Q_T$ and $Ω$ respectively and $g(u) \sim e^{a |u|^q} $ with $a>0$ and $q \geq 1$. We provide a sufficient condition in terms of fractional maximal potentials of $μ$ and $ω$ for solving (P).