Differential and Integral Equations

Quasilinear evolution equations with non-densely defined operators

Naoki Tanaka

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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

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

First available in Project Euclid: 6 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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