Entropy solutions for parabolic equations in Musielak framework without sign condition and with measure data

M.S.B. Elemine Vall, A. Ahmed, A. Touzani, and A. Benkirane

Address: Corresponding author: Mohamed Saad Bouh ELEMINE VALL, University of Sidi Mohamed Ibn Abdellah, Faculty of Sciences Dhar El Mahraz, Laboratory LAMA, Department of Mathematics, B.P. 1796 Atlas Fez, Morocco

E-mail:
saad2012bouh@gmail.com
ahmedmath2001@gmail.com
atouzani07@gmail.com
abd.benkirane@gmail.com

Abstract: We prove an existence result of entropy solutions for a class of strongly nonlinear parabolic problems in Musielak-Sobolev spaces, without using the sign condition on the nonlinearities and with measure data.

AMSclassification: primary 46E35; secondary 80M10, 35K55.

Keywords: inhomogeneous Musielak-Orlicz-Sobolev spaces, parabolic problems, Galerkin method.

DOI: 10.5817/AM2020-2-65