A final value problem for heat equation: regularization by truncation method and new error estimates.
A generalization of the maximal entropy method for solving ill-posed problems.
A simple regularization method for the ill-posed evolution equation
The nonhomogeneous backward Cauchy problem , where is a positive self-adjoint unbounded operator which has continuous spectrum and is a given function being given is regularized by the well-posed problem. New error estimates of the regularized solution are obtained. This work extends earlier results by N. Boussetila and by M. Denche and S. Djezzar.
Degeneracy in the Blasius problem.
General regularizing functionals for solving ill-posed problems in Lebesgue spaces.
Ill-posedness for the Navier-Stokes and Euler equations in Besov spaces
We construct a new initial data to prove the ill-posedness of both Navier-Stokes and Euler equations in weaker Besov spaces in the sense that the solution maps to these equations starting from are discontinuous at .
Newton-type iterative methods for nonlinear ill-posed Hammerstein-type equations
We use a combination of modified Newton method and Tikhonov regularization to obtain a stable approximate solution for nonlinear ill-posed Hammerstein-type operator equations KF(x) = y. It is assumed that the available data is with , K: Z → Y is a bounded linear operator and F: X → Z is a nonlinear operator where X,Y,Z are Hilbert spaces. Two cases of F are considered: where exists (F’(x₀) is the Fréchet derivative of F at an initial guess x₀) and where F is a monotone operator. The parameter...
On an initial inverse problem in nonlinear heat equation associated with time-dependent coefficient
In this paper, a nonlinear backward heat problem with time-dependent coefficient in the unbounded domain is investigated. A modified regularization method is established to solve it. New error estimates for the regularized solution are given under some assumptions on the exact solution.
On the semilocal convergence of a two-step Newton-like projection method for ill-posed equations
We present new semilocal convergence conditions for a two-step Newton-like projection method of Lavrentiev regularization for solving ill-posed equations in a Hilbert space setting. The new convergence conditions are weaker than in earlier studies. Examples are presented to show that older convergence conditions are not satisfied but the new conditions are satisfied.
Regularization and error estimates for nonhomogeneous backward heat problems.
Regularization and new error estimates for a modified Helmholtz equation.
Regularization of nonlinear ill-posed equations with accretive operators.
Regularization properties of Tikhonov regularization with sparsity constraints.
Stabilized quasi-reversibility method for a class of nonlinear ill-posed problems.