Parabolic equations with exponential nonlinearity and measure data

2013/12/09 by Nguyen, Phuoc-Tai
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1312.2509

Abstract

Let Ω be a bounded domain in \mathbb R^N and T>0. We study the problem (P)\ u_t - Δu ± g(u) · amp;= μ · amp;in Q_T:=Ω× (0,T)
\phantom------, u · amp;=0 · amp;on ∂ Ω× (0,T)
\phantom----, u(.,0) · amp;=ω · amp;in Ω. . where μ and ω are bounded Radon measures in Q_T and Ω respectively and g(u) ∼ e^{a |u|q} with a>0 and q ≥ 1. We provide a sufficient condition in terms of fractional maximal potentials of μ and ω for solving (P).

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