Page 1

Displaying 1 – 1 of 1

Showing per page

Truncated spectral regularization for an ill-posed non-linear parabolic problem

Ajoy Jana, M. Thamban Nair (2019)

Czechoslovak Mathematical Journal

It is known that the nonlinear nonhomogeneous backward Cauchy problem u t ( t ) + A u ( t ) = f ( t , u ( t ) ) , 0 t < τ with u ( τ ) = φ , where A is a densely defined positive self-adjoint unbounded operator on a Hilbert space, is ill-posed in the sense that small perturbations in the final value can lead to large deviations in the solution. We show, under suitable conditions on φ and f , that a solution of the above problem satisfies an integral equation involving the spectral representation of A , which is also ill-posed. Spectral truncation is used...

Currently displaying 1 – 1 of 1

Page 1