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 of diffusion coefficients 5 Piece Outdoor Sectional with Tables {bi(x)} ${b_{i}(x)}$ are degenerate on the boundary, the others are always positive, then how to impose a suitable Knife tower 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, is established by choosing a suitable test function.