Taiwanese Journal of Mathematics


Naoki Tanaka

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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

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

First available in Project Euclid: 21 July 2017

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Zentralblatt MATH identifier

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

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


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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