1996 Quasilinear evolution equations with non-densely defined operators
Naoki Tanaka
Differential Integral Equations 9(5): 1067-1106 (1996). DOI: 10.57262/die/1367871531

Abstract

Two problems for the abstract quasilinear evolution equation of "hyperbolic" type in a Banach space $$ u'(t) = A(t,u(t))u(t) \,\,\,\rm{for} \,\,\,t \geq 0, \,\,\, \rm{and} \,\,\, u(0)=u_0 $$ are studied without assuming that the domain of $A(t,w)$ is dense in the whole space. One is the fundamental problem of existence and uniqueness of classical solutions, and the other is the problem of extension or blow up of classical solutions.

Citation

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Naoki Tanaka. "Quasilinear evolution equations with non-densely defined operators." Differential Integral Equations 9 (5) 1067 - 1106, 1996. https://doi.org/10.57262/die/1367871531

Information

Published: 1996
First available in Project Euclid: 6 May 2013

zbMATH: 0942.34053
MathSciNet: MR1392095
Digital Object Identifier: 10.57262/die/1367871531

Subjects:
Primary: 34G20
Secondary: 47H20

Rights: Copyright © 1996 Khayyam Publishing, Inc.

Vol.9 • No. 5 • 1996
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