具有一般测度数据的非线性抛物型方程的重整化解
偏微分方程分析
2014-09-22 v1
摘要
设 Ω ⊆ R N \Omega\subseteq \mathbb{R}^N Ω ⊆ R N N ≥ 2 N\geq 2 N ≥ 2 p > 1 p>1 p > 1 { u t − Δ p u = μ in ( 0 , T ) × Ω , u ( 0 , x ) = u 0 in Ω , u ( t , x ) = 0 on ( 0 , T ) × ∂ Ω , \begin{cases} u_{t}-\Delta_{p} u=\mu & \text{in}\ (0,T)\times\Omega,\newline u(0,x)=u_0 & \text{in}\ \Omega,\newline u(t,x)=0 &\text{on}\ (0,T)\times\partial\Omega, \end{cases} ⎩ ⎨ ⎧ u t − Δ p u = μ u ( 0 , x ) = u 0 u ( t , x ) = 0 in ( 0 , T ) × Ω , in Ω , on ( 0 , T ) × ∂ Ω , T > 0 T>0 T > 0 μ ∈ M ( Q ) \mu\in M(Q) μ ∈ M ( Q ) Q = ( 0 , T ) × Ω Q=(0,T)\times\Omega Q = ( 0 , T ) × Ω u o ∈ L 1 ( Ω ) u_o\in L^1(\Omega) u o ∈ L 1 ( Ω ) − Δ p u = − d i v ( ∣ ∇ u ∣ p − 2 ∇ u ) -\Delta_{p} u=-{\rm div} (|\nabla u|^{p-2}\nabla u ) − Δ p u = − div ( ∣∇ u ∣ p − 2 ∇ u ) p p p
引用
@article{arxiv.1409.5575,
title = {Renormalized solutions of nonlinear parabolic equations with general measure data},
author = {Francesco Petitta},
journal= {arXiv preprint arXiv:1409.5575},
year = {2014}
}