Abstract The anisotropic parabolic equations with variable exponents are considered.If some of diffusion swish supreme glide track white 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 here 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.