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Doubly Nonlinear Parabolic P.D.E.s

  • Augusto Visintin
Chapter
  • 306 Downloads
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 28)

Abstract

Existence results are derived for (possibly degenerate) doubly nonlinear parabolic equations, in particular
$$\begin{array}{*{20}c} {\frac{\partial } {{\partial t}}\alpha (u) - \nabla \cdot \vec \gamma (\nabla u) \mathrel\backepsilon f,} & {\alpha \frac{{\partial u}} {{\partial t}} - \nabla \cdot \vec \gamma (\nabla u) \mathrel\backepsilon f,} \\ {\frac{\partial } {{\partial t}}\alpha (u) - \nabla \cdot \tilde \gamma (\nabla u) \mathrel\backepsilon f,} & {\alpha \frac{{\partial u}} {{\partial t}} - \nabla \cdot \tilde \gamma (\nabla u) \mathrel\backepsilon f;} \\ \end{array} $$
here \(\alpha ,\,\tilde \gamma :R \to \text{2}^\text{R}\) and \(\vec \gamma \,\text{:}\,R^N \to 2^{(R^N )}\) are maximal monotone operators.

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Copyright information

© Birkhäuser Boston 1996

Authors and Affiliations

  • Augusto Visintin
    • 1
  1. 1.Dipartimento di MatematicaUniversità Degli Studi di TrentoPovoItaly

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