Displaying similar documents to “Uniqueness and stability of solutions for a type of parabolic boundary value problem.”

The BV solution of the parabolic equation with degeneracy on the boundary

Huashui Zhan, Shuping Chen (2016)

Open Mathematics

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Consider a parabolic equation which is degenerate on the boundary. By the degeneracy, to assure the well-posedness of the solutions, only a partial boundary condition is generally necessary. When 1 ≤ α < p – 1, the existence of the local BV solution is proved. By choosing some kinds of test functions, the stability of the solutions based on a partial boundary condition is established.