Existence of entropy solutions to nonlinear degenerate parabolic problems with variable exponent and L ¹-data

Abstract

In the present paper, we prove existence results of entropy solutions to a class of nonlinear degenerate parabolic p(·)-Laplacian problem with Dirichlet-type boundary conditions and L 1 data. The main tool used here is the Rothe method combined with the theory of variable exponent Sobolev spaces.(1) 2020 MSC: 35A02, 35J60, 35J65, 35J92

The Existence of Entropy Solutions for a Class of Parabolic Equations

“…The results on both elliptic and parabolic equations involving a variable exponent have kept growing in recent years. We refer to the references [4][5][6][7][8][9][10][11][12].…”

Weak Solution for Nonlinear Fractional P(.)-Laplacian Problem With Variable Order via Rothe's Time-Discretization Method

“…Mosolov, K. Rektorys in linear and quasilinear parabolic problems. This method has been used by several authors while studying time discretization of nonlinear parabolic problems, we refer to the works [12,21,22] for some details. The advantage of our method is that we cannot only obtain the existence and uniqueness of weak solutions to the problem (1.1), but also compute the numerical approximations.…”

A parabolic problem involving $p(x)$-Laplacian, a power and a singular nonlinearity

“…In the same spirit of [10], in [32] the authors have shown the existence of a weak solution by considering g to be in L 1 (Q T ) and by replacing the function f with a bounded Radon measure µ. The parabolic problems involving p(x)-Laplacian and a measure data or an L 1 data (the case λ = 0 and g ≡ 0 of (1.1)) have been analyzed by several authors since the papers [5,38,42]. The corresponding constant exponent cases (problems with p-Laplacian) are studied by Petitta et al in [35,36] and Boccardo et al in [7,6], etc.…”