A non-local boundary value problem method for semi-linear parabolic equations backward in time

Abstract

The ill-posed semi-linear parabolic equation backward in time with the positive self-adjoint unbounded linear operator A and being given is regularized by the well-posed non-local boundary value problem Under the condition , a priori and a posteriori parameter choice rules are suggested which yield the error estimate for some positive constant C.

Keywords:

• semi-linear parabolic equations backward in time
• ill-posed problems
• regularization
• non-local boundary value problems

AMS Subject Classifications:

• Primary: 35R25
• 35R30
• 47J06
• Secondary: 35K58
• 65N20
• 65N21

Notes

Dedicated to Professor Bernd Hofmann on the occasion of his sixtieth birthday.

This research was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) [grant number 101.02-2014.54]; Vietnam Ministry of Education and Training [grant number B2013-27-09].