Ninth MSUUAB Conference on Differential Equations and Computational Simulations.
Electron. J. Diff. Eqns., Conference 20 (2013), pp. 6578.
Modified quasireversibility method for nonautonomous semilinear problems
Matthew A. Fury
Abstract:
We prove regularization for the illposed, semilinear evolution
problem
,
,
with initial condition
in a Hilbert space where D
is a positive, selfadjoint operator in the space.
As in recent literature focusing on linear equations, regularization
is established by approximating a solution u(t) of the problem by
the solution of an approximate wellposed problem.
The approximate problem will be defined by one specific approximation
of the operator A(t,D) which extends a recently introduced,
modified quasireversibility method by Boussetila and Rebbani.
Finally, we demonstrate our theory with applications to a wide class
of nonlinear partial differential equations in
spaces including
the nonlinear backward heat equation with a timedependent diffusion
coefficient.
Published October 31, 2013.
Math Subject Classifications: 46C05, 47D06.
Key Words: Regularization for illposed problems;
semilinear evolution equation; backward heat equation.
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Matthew Fury
Division of Science & Engineering,
Penn State Abington
1600 Woodland Road
Abington, PA 19001, USA
email: maf44@psu.edu, Tel: 2158817553, Fax: 2158817333

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