On a double degenerate fourth-order parabolic equation |
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Authors: | Bo Liang Caiyue Su Ying Wang |
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Institution: | School of Science, Dalian Jiaotong University, Dalian 116028, PR China |
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Abstract: | The existence of solutions to a fourth-order p-Laplacian equation with boundary degeneracy is studied. For the purpose of solving the corresponding non-degenerate (with respect to the coefficient of fourth-order term) regularized problem, a fourth-order semi-discrete elliptic problem with homogeneous boundary conditions is established and its existence and uniqueness are obtained by the functional minimization method. It follows that the approximate solutions of the non-degenerate parabolic problem are constructed and the corresponding existence and uniqueness are discovered by a limit procedure from the energy estimation method and a compactness argument. Finally, the existence and regularity of solutions for the problem with boundary degeneracy is obtained by using a regularization parameter vanishing limit. |
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Keywords: | Fourth-order parabolic Fourth-order degenerate Boundary degeneracy Double degeneracy |
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