Long-time behavior of small solutions to quasilinear dissipative hyperbolic equations

Albert Milani, Hans Volkmer

Research output: Contribution to journalArticle

Abstract

We give sufficient conditions for the existence of global small solutions to the quasilinear dissipative hyperbolic equation u t t+2u t-a ij(u tu) α iα ju=f corresponding to initial values and source terms of sufficiently small size, as well as of small solutions to the corresponding stationary version, i.e. the quasilinear elliptic equation -a ij(0,v)α iα jv = h.We then give conditions for the convergence, as t-∞, of the solution of the evolution equation to its stationary state.

Original languageEnglish
Pages (from-to)425-457
Number of pages33
JournalApplications of Mathematics
Volume56
Issue number5
DOIs
Publication statusPublished - Oct 1 2011

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Small Solutions
Dissipative Equations
Long-time Behavior
Hyperbolic Equations
Quasilinear Elliptic Equation
Stationary States
Source Terms
Evolution Equation
Sufficient Conditions

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Cite this

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Long-time behavior of small solutions to quasilinear dissipative hyperbolic equations. / Milani, Albert; Volkmer, Hans.

In: Applications of Mathematics, Vol. 56, No. 5, 01.10.2011, p. 425-457.

Research output: Contribution to journalArticle

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