MMN-284
Regularization for a nonlinear backward parabolic problem with continuous spectrum operator
Abstract
We study the backward parabolic problem for a nonlinear parabolic equation of the form $u_t +Au(t) = f(t,u(t)),u(T) = varphi$, where $A$ is a positive self-adjoint unbounded operator and $f $ is a Lipschitz function. The problem is ill-posed, in the sense that if the solution does exist, it will not depend continuously on the data. To regularize the problem, we use the quasi-boundary method and the quasi-reversibility method to establish a modified problem. We present approximated solutions that depend on a small parameter $epsilopn>0$ and give error estimates for our regularization.
Vol. 14 (2013), No. 1, pp. 291-306
DOI: 10.18514/MMN.2013.284