Existence theorems for solutions of parabolic equations with variable order of nonlinearity
Yu. A. Alkhutov, Vasilii Vasil'evich Zhikov · Proceedings of the Steklov Institute of Mathematics · 2010
We study the solvability of an initial-boundary value problem for second-order parabolic equations with variable order of nonlinearity. In the model case, the equation contains the p -Laplacian with a variable exponent p ( x, t ). We prove that if the measurable exponent p is separated from unity and infinity, then the problem has W -and H -solutions.