Existence and uniqueness theorems for solutions of parabolic equations with a variable nonlinearity exponent
Yu. A. Alkhutov, Vasilii Vasil'evich Zhikov · Sbornik Mathematics · 2014
The paper is concerned with the solvability of the initial-boundary value problem for second-order parabolic equations with variable nonlinearity exponents. In the model case, this equation contains the -Laplacian with a variable exponent . The problem is shown to be uniquely solvable, provided the exponent is bounded away from both 1 and and is log-Holder continuous, and its solution satisfies the energy equality. Bibliography: 18 titles.