RENORMALIZED AND ENTROPY SOLUTIONS TO THE GENERAL NONLINEAR PARABOLIC EQUATIONS IN MUSIELAK–ORLICZ SPACES
Abstract
Abstract We study the well-posedness of solutions to the general nonlinear parabolic equations with merely integrable data in time-dependent Musielak–Orlicz spaces. With the help of a density argument, we establish the existence and uniqueness of both renormalized and entropy solutions. Moreover, we conclude that the entropy and renormalized solutions for this equation are equivalent. Our results cover a variety of problems, including those with Orlicz growth, variable exponents and double-phase growth.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Geometric Analysis and Curvature Flows
Differential Equations and Boundary Problems
Publication details
- Journal / source
- Journal of the Australian Mathematical Society
- Volume
- 120
- Issue
- 3
- Pages
- 394–423
- Publication date
- 30 January 2026
- Language
- EN