Taiwanese Journal of Mathematics

APPROXIMATION OF ABSTRACT QUASILINEAR EVOLUTION EQUATIONS IN THE SENSE OF HADAMARD

Naoki Tanaka

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Abstract

An approximation theorem is given for abstract quasilinear evolution equations in the sense of Hadamard. A stability condition is proposed under which a sequence of approximate solutions converges to the solution. The result obtained in this paper is a generalization of an approximation theorem of regularized semigroups and is applied to an approximation problem for a degenerate Kirchhoff equation.

Article information

Source
Taiwanese J. Math., Volume 12, Number 3 (2008), 767-792.

Dates
First available in Project Euclid: 21 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500602434

Digital Object Identifier
doi:10.11650/twjm/1500602434

Mathematical Reviews number (MathSciNet)
MR2417147

Zentralblatt MATH identifier
1161.34032

Subjects
Primary: 34G20: Nonlinear equations [See also 47Hxx, 47Jxx]
Secondary: 47D60: $C$-semigroups, regularized semigroups

Keywords
Hadamard well-posedness quasi-linear evolution equation regularized semigroup abstract Cauchy problem stability condition consistency condition

Citation

Tanaka, Naoki. APPROXIMATION OF ABSTRACT QUASILINEAR EVOLUTION EQUATIONS IN THE SENSE OF HADAMARD. Taiwanese J. Math. 12 (2008), no. 3, 767--792. doi:10.11650/twjm/1500602434. https://projecteuclid.org/euclid.twjm/1500602434


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