Nonlinear parabolic equations with nonstandard growth. Issue 12 (1st December 2016) - Youssfi, A.; Azroul, E.; Lahmi, B.
Abstract : In this paper, we study the solvability of the initial-boundary value problem for second-order nonlinear parabolic equations with nonstandard growth conditions and -source terms. In the model case, these equations include the p -Laplacian with a variable exponent p ( x,   t ). We prove that if the variable exponent p is bounded away from both 1 and and is log-Hölder continuous, then the problem has a weak solution which satisfies the energy equality.