6533b7d8fe1ef96bd126b62d
RESEARCH PRODUCT
Quasi-linear diffusion equations with gradient terms and L1 data
Fuensanta AndreuSergio Segura De LeónJulián Toledosubject
Partial differential equationApplied MathematicsBounded functionMathematical analysisOpen setParabolic problemQuasi linearDiffusion (business)AnalysisMathematicsdescription
Abstract In this article we study the following quasi-linear parabolic problem: u t − Δ u+|u| β−2 u| ∇ u| q =|u| α−2 u| ∇ u| p in Ω×]0,T[, u(x,t)=0 on ∂Ω×]0,T[, u(x,0)=u 0 (x) in Ω, where Ω is a bounded open set of R N and T>0. We prove that if α,β>1, 0⩽p u 0 ∈L 1 (Ω) .
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2004-03-01 | Nonlinear Analysis: Theory, Methods & Applications |