We study the homogeneous Dirichlet problem for the parabolic equations ut− div (A (z,∣∇
u∣)∇ u)= F (z, u,∇ u), z=(x, t)∈ Ω×(0, T), with the double phase flux A (z,∣∇ u∣)∇ …

We investigate the existence of a time-periodic solution to a nonlinear evolution equation
involving p (x)-growth conditions with irregular data. We tackle our problem in a suitable …

We consider a parabolic PDE with Dirichlet boundary condition and monotone operator A
with non-standard growth controlled by an N-function depending on time and spatial …

This article establishes an interior gradient higher integrability result for weak solutions to
parabolic multi-phase problems. The prototype equation for the parabolic multi-phase …

In Ω ⊂ R n \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}
\usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} …

We study the homogeneous Dirichlet problem for the equation ut-div F (z,∇ u)∇ u= f, z=(x,
t)∈ QT= Ω×(0, T), where Ω⊂ RN, is a bounded domain with∂ Ω∈ C 2, and F (z, ξ)= a (z)| ξ …

In this paper, we study quasilinear parabolic equations with the nonlinearity structure
modeled after the p (x, t)-Laplacian on nonsmooth domains. The main goal is to obtain end …

This article proves an interior gradient higher integrability result for weak solutions to the
parabolic double phase problems. The prototype equation for the parabolic double phase …

In this paper, we are interested in obtaining a unified approach for $ C^{1,\alpha} $
estimates for weak solutions of quasilinear parabolic equations, the prototype example …

In the first part, the author considers the fast reaction limit for a system of reactiondiffusion
equations where the reaction function is non-monotone. This limit is much simpler when the …