Displaying similar documents to “Some qualitative problems in the theory of second order partial differential equations”

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.