On a backward Cauchy problem associated with continuous spectrum operator Original Research Article

The nonlinear backward Cauchy problem ut+Au(t)=f(u(t)),u(T)=φ,ut+Au(t)=f(u(t)),u(T)=φ, Turn MathJax on where AA is a positive self-adjoint unbounded operator, which has a continuous spectrum and ff is a Lipschitz function being given is regularized by the well-posed problem. The new error estimates of the regularized solution are obtained. This work extends to the nonlinear case earlier results by the authors and and by Denche and Bessila and .