Sobolev regularity for t > 0 in quasilinear parabolic equations

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We establish a regularity property for the solutions to the quasilinear parabolic initial-boundary value problem (1.4) below, showing that for t > 0 they belong to the same space to which the solutions of the second order hyperbolic problem (1.5), which is a singular perturbation of (1.4), belong. This result provides another illustration of the asymptotically parabolic nature of problem (1.5), and would be needed to establish the diffusion phenomenon for quasilinear dissipative wave equations in Sobolev spaces.

Original languageEnglish
Pages (from-to)113-127
Number of pages15
JournalMathematische Nachrichten
Volume231
DOIs
Publication statusPublished - Jan 1 2001

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Quasilinear Parabolic Equations
Regularity
Dissipative Equations
Hyperbolic Problems
Regularity Properties
Singular Perturbation
Parabolic Problems
Initial-boundary-value Problem
Sobolev Spaces
Wave equation

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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abstract = "We establish a regularity property for the solutions to the quasilinear parabolic initial-boundary value problem (1.4) below, showing that for t > 0 they belong to the same space to which the solutions of the second order hyperbolic problem (1.5), which is a singular perturbation of (1.4), belong. This result provides another illustration of the asymptotically parabolic nature of problem (1.5), and would be needed to establish the diffusion phenomenon for quasilinear dissipative wave equations in Sobolev spaces.",
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Sobolev regularity for t > 0 in quasilinear parabolic equations. / Milani, Albert.

In: Mathematische Nachrichten, Vol. 231, 01.01.2001, p. 113-127.

Research output: Contribution to journalArticle

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