Resumen de Energy Solutions of Evolution Equations with Nonstandard Growth Conditions

S. Antontsev, Sergey Shmarev Jigulev

• We present an overview of the recent advances in the theory of parabolic equations with nonstandard anisotropic growth conditions. The presentation includes the existence theorems in the variable exponents Sobolev spaces and a description of the properties of propagation of disturbances from the data, intrinsic for solutions of such equations.