Degenerate quasilinear pseudoparabolic equations with memory terms and variational inequalities |
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Authors: | Mariya Ptashnyk |
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Institution: | Institute of Applied Mathematics, University of Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany |
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Abstract: | The existence of solutions of degenerate quasilinear pseudoparabolic equations, where the term ∂tu is replace by ∂tb(u), with memory terms and quasilinear variational inequalities is shown. The existence of solutions of equations is proved under the assumption that the nonlinear function b is monotone and a gradient of a convex, continuously differentiable function. The uniqueness is proved for Lipschitz-continuous elliptic parts. The existence of solutions of quasilinear variational inequalities is proved under stronger assumptions, namely, the nonlinear function defining the elliptic part is assumed to be a gradient and the function b to be Lipschitz continuous. |
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Keywords: | 35K55 35K60 35K70 35K85 35R45 |
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