LONG-TIME BEHAVIOR OF SMALL SOLUTIONS TO QUASILINEAR DISSIPATIVE HYPERBOLIC EQUATIONS

Journal article

Authors/Editors

Milani, Albert

Research Areas

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Publication Details

Author list: Milani A, Volkmer H

Publisher: Springer

Place: PRAHA 1

Publication year: 2011

Journal: Applications of Mathematics (0862-7940)

Journal acronym: APPL MATH-CZECH

Volume number: 56

Issue number: 5

Start page: 425

End page: 457

Number of pages: 33

ISSN: 0862-7940

eISSN: 1572-9109

Languages: English-Great Britain (EN-GB)

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Abstract

We give sufficient conditions for the existence of global small solutions to the quasilinear dissipative hyperbolic equationu(tt) + 2u(t) - a(ij)(u(t),del u)partial derivative(i)partial derivative(j)u = fcorresponding 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,del v)partial derivative(i)partial derivative(j)v = hWe then give conditions for the convergence, as t -> infinity, of the solution of the evolution equation to its stationary state.

Keywords

A priori estimates, Asymptotic behavior, Global existence, quasilinear elliptic equation, quasilinear evolution equation, stationary solutions

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