Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4620847 | Journal of Mathematical Analysis and Applications | 2008 | 11 Pages |
Abstract
In this work we study the global existence of a solution to some parabolic problems whose model isequation(1){ut−Δu=g(u)+μ,(x,t)∈Ω×(0,∞),u(x,t)=0,(x,t)∈∂Ω×(0,∞),u(x,0)=u0(x),x∈Ω, where Ω⊂RNΩ⊂RN is a bounded domain, u0∈L1(Ω)u0∈L1(Ω), μ is a finite Radon measure in Ω×(0,∞)Ω×(0,∞) and g is a real continuous function, slightly superlinear at infinity (“slightly” in the sense that 1/g1/g is not integrable at ∞). One of the main tools is a new logarithmic Sobolev inequality. We also prove some uniqueness results.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Andrea Dall'Aglio, Daniela Giachetti, Ireneo Peral, Sergio Segura de León,