A modified quasi-boundary value method for ill-posed problems

By M. Denche, K. Bessila. 2005

158 citations recorded by the source corpus.

In this paper, we study a final value problem for first order abstract differential equation with positive self-adjoint unbounded operator coefficient. This problem is ill-posed. Perturbing the final condition we obtain an approximate nonlocal problem depending on a small parameter. We show that the approximate problems are well posed and that their solutions converge if and only if the original problem has a classical solution. We also obtain estimates of the solutions of the approximate problems and a convergence result of these solutions. Finally, we give explicit convergence rates.

Subfields: Applied Mathematics, Mathematical Physics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/72b02367936eb9fc2fc23c12156c5eb49f6e1fea

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Phan Thanh Nam
2. Huy Tuan Nguyen
3. Dang Duc Trong
4. Nguyen Huy Tuan
5. Duc Trong Dang

In Mathematical Physics

1. Phan Thanh Nam
2. Nguyen Huy Tuan
3. Dang Duc Trong
4. Huy Tuan Nguyen
5. Duc Trong Dang

In Mechanics of Materials

1. Phan Thanh Nam
2. Dang Duc Trong
3. Nguyen Huy Tuan

Citations in the corpus

• An approximate solution for nonlinear backward parabolic equations (2010, methodology): “Note that the assumption u(0) ∈ D(A) in [1] is a special case of (1.”
• A NONHOMOGENEOUS BACKWARD HEAT PROBLEM: REGULARIZATION AND ERROR ESTIMATES (2008, methodology): “Using the method, Clark and Oppenheimer, in [4], and Denche-Bessila, very recently in [ 5 ], regularized the backward problem by replacing the final condition by”
• REGULARIZATION AND ERROR ESTIMATES FOR NONHOMOGENEOUS BACKWARD HEAT PROBLEMS (2006, background): “[7] M. Denche, and K. Bessila, A modified quasi-boundary value method for ill-posed problems, J. Math.”