A modified quasi-boundary value method for a class of abstract parabolic ill-posed problems
<p/> <p>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 th...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2006-01-01
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| Series: | Boundary Value Problems |
| Online Access: | http://www.boundaryvalueproblems.com/content/2006/37524 |
| Summary: | <p/> <p>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.</p> |
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| ISSN: | 1687-2762 1687-2770 |