Differential and Integral Equations

Quasilinear evolution equations with non-densely defined operators

Naoki Tanaka

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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.

Article information

Source
Differential Integral Equations, Volume 9, Number 5 (1996), 1067-1106.

Dates
First available in Project Euclid: 6 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367871531

Mathematical Reviews number (MathSciNet)
MR1392095

Zentralblatt MATH identifier
0942.34053

Subjects
Primary: 34G20: Nonlinear equations [See also 47Hxx, 47Jxx]
Secondary: 47H20: Semigroups of nonlinear operators [See also 37L05, 47J35, 54H15, 58D07]

Citation

Tanaka, Naoki. Quasilinear evolution equations with non-densely defined operators. Differential Integral Equations 9 (1996), no. 5, 1067--1106. https://projecteuclid.org/euclid.die/1367871531


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