Electron. J. Diff. Equ.,
Vol. 2011 (2011), No. 92, pp. 130.
Timedependent domains for nonlinear evolution operators and
partial differential equations
ChinYuan Lin
Abstract:
This article concerns the nonlinear evolution equation
in a real Banach space X, where the nonlinear, timedependent,
and multivalued operator
has a timedependent domain D(A(t)).
It will be shown that, under certain assumptions on A(t),
the equation has a strong solution. Illustrations are
given of solving quasilinear partial differential equations
of parabolic type with timedependent boundary conditions.
Those partial differential equations are studied to a
large extent.
Submitted June 15, 2011. Published July 18, 2011.
Math Subject Classifications: 47B44, 47H20, 35J25, 35K20.
Key Words: Dissipative operators; evolution equations;
parabolic and elliptic equations.
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ChinYuan Lin
Department of Mathematics
National Central University
ChungLi 320, Taiwan
email: cylin@math.ncu.edu.tw

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