Existence of renormalized solutions to non-linear $p(\cdot)$-parabolic problems of generalized porous medium with general measure data

Abdelaziz Sabiry; Ghizlane  Zineddaine; Abderrazak  Kassidi; Said  Melliani

doi:10.5269/bspm.69752

Existence of renormalized solutions to non-linear $p(\cdot)$-parabolic problems of generalized porous medium with general measure data

Abdelaziz Sabiry Laboratory LMACS, Sultan Moulay Slimane University
Ghizlane Zineddaine Laboratory LMACS, Sultan Moulay Slimane University,
Abderrazak Kassidi Laboratory LMACS, Sultan Moulay Slimane University
Said Melliani Laboratory LMACS, Sultan Moulay Slimane University,

Abstract

In this work, we investigate the existence of renormalized solutions for a nonlinear parabolic problem with variable exponents and general measure data. The solutions are achieved by combining monotone operator theory, Marcinkiewicz estimation, and the truncation method.