Research
Communication | Open Access
Volume 2021 | Communication ID 30
Volume 2021 | Communication ID 30
Regularity results of some perturbed problems |
Mohammed Abdellaoui, Hicham Redwane
Received |
Accepted |
Published |
May 01, 2021 |
May 10, 2021 |
July 15, 2021 |
Abstract: In this paper, we study a class of nonlinear parabolic problems whose simplest model is given by (P_1) u_t-div[a(t,x,u)(1+|u|)^m |∇u|^(p-2) ∇u]=μ in Q≔(0,T)×Ω, u(t,x)=0 on (0,T)×∂Ω, u(0,x)=u_0 (x) in Ω, where Ω is a bounded open set in R^N (N≥2), T>0, the vector filed α≤a(t,x,u)≤β (for some constants α,β>0), m≥0, u_0∈L^1 (Ω) and μ is a bounded Radon measure on Q. We show, under which condition on m, problem (P_1) admits a solution and we prove some regularity results. Moreover, in presence of a lower order (perturbed) term with ...