On some nonlinear parabolic equations with variable exponents and measure data

Abstract

We prove the existence of renormalized solutions to a class of nonlinear evolution equations, supplemented with initial and Dirichlet condition in the framework of generalized Sobolev spaces. The data are assumed merely integrable.

Keywords

• parabolic problems
• sobolev space with variable exponent
• renormalized solutions
• primary 47a15
• secondary 46a32
• 47d20