Elliptic approximation of forward-backward parabolic equations

Fabio Paronetto

doi:10.3934/cpaa.2020047

Article Contents

2020, Volume 19, Issue 2: 1017-1036. Doi: 10.3934/cpaa.2020047

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Elliptic approximation of forward-backward parabolic equations

Fabio Paronetto

Dipartimento di Matematica Tullio Levi Civita, Università degli Studi di Padova, Via Trieste 63 - Padova, Italy

Received: February 28, 2018

Revised: May 31, 2019

Published: October 2019

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Abstract

In this note we give existence and uniqueness result for some elliptic problems depending on a small parameter and show that their solutions converge, when this parameter goes to zero, to the solution of a mixed type equation, elliptic-parabolic, parabolic both forward and backward. The aim is to give an approximation result via elliptic equations of a changing type equation.

Keywords:

Abstract equations,
elliptic equations,
elliptic-parabolic equations,
forward-backward parabolic equations,
monotone operators,
approximation by singular perturbations.

Mathematics Subject Classification: 35J60, 35M10, 35K90, 34D15.

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References

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