Parabolic problems in R n with spatially variable exponents
Claudianor O. Alves, Jacson Simsen, Mariza Stefanello Simsen · Asymptotic Analysis · 2015
We study the asymptotic behavior of parabolic p(x)-Laplacian problems of the form ∂uλ∂t−div(Dλ|∇uλ|p(x)−2∇uλ)+a|uλ|p(x)−2uλ=B(uλ) in L2(Rn), where n⩾1, p∈L∞(Rn) such that 2 M⩾Dλ(x)⩾σ>0 a.e. in Rn, λ∈[0,∞), B:L2(Rn)→L2(Rn) is a glo bally Lipschitz map and a:Rn→R is a non-negative continuous function such that there exists R1>0 with {x∈Rn;a(x)=0}⊂BR1(0), infx∈Rn∖BR1(0)a(x)>0, and ∫Rn∖BR1(0)1a(x)2/(p(x)−2)dx<+∞. We also study the sensitivity of the problem according to the variation of the diffusion coefficients.