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.
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