On stability with respect to boundary conditions for anisotropic parabolic equations with variable exponents

On stability with respect to boundary conditions for anisotropic parabolic equations with variable exponents

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Abstract The anisotropic parabolic equations with variable exponents are considered.If some click here of diffusion coefficients {bi(x)} ${b_{i}(x)}$ are degenerate on the boundary, the others are always positive, then how to impose a suitable boundary value condition is researched.The existence of weak solutions is proved by the parabolically regularized method.The stability of weak solutions, based on the partial boundary value condition, superdry baseball top is established by choosing a suitable test function.