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Sur le comportement asymptotique des bonnes solutions d'une classe de problèmes paraboliques dégénérés du type Neumann

Abstract : The study set fort.h in this thes is concerns the long-time behavior of certain solutions to a class of nonlinear degenerate parabolic equations. The equations that we investigate play an important role in the analysis of certain phenomella related to the nonlinear diffusion of substances through porous media; they also play a role in plasma physics, in population dynamics and in many other applications. ln the first chapter we explain briefly what is already known regarding the problem under consideration, and we explain the strategy and the methods we wish to use to prove some generalizations. In the second chapter we formulate precisely and we discuss all of our results which concern the long-time behavior of solutions to problems of fast and slow diffusion. In the third chapter, we give the complete proofs of all our results. The techniques that we use combine methods from the theory of nonlinear semigroups and from the theory of infinite-dimensional dynamical systems. An important feature of our work is t.hat we are able to exhibit the rate of decay of the solutions in each case we consider. These rates of convergence can be either exponential or polynomial, and which one occurs depends on the structural properties of the nonlinearities and of the initial conditions involved .
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https://hal.univ-lorraine.fr/tel-01747438
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Submitted on : Thursday, March 29, 2018 - 10:59:57 AM
Last modification on : Saturday, October 16, 2021 - 11:18:03 AM

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  • HAL Id : tel-01747438, version 1

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Mimoun Benmimoun. Sur le comportement asymptotique des bonnes solutions d'une classe de problèmes paraboliques dégénérés du type Neumann. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 1997. Français. ⟨NNT : 1997NAN10252⟩. ⟨tel-01747438⟩

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