## Taiwanese Journal of Mathematics

### APPROXIMATION OF ABSTRACT QUASILINEAR EVOLUTION EQUATIONS IN THE SENSE OF HADAMARD

Naoki Tanaka

#### 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

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
Secondary: 47D60: $C$-semigroups, regularized semigroups

#### 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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