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Uravneniya matematicheskoi fiziki (dop. gl.) (Equations of Mathematical Physics
- Publisher
- Springer Journals
- Copyright
- Copyright © 2015 by Pleiades Publishing, Ltd.
- Subject
- Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
- ISSN
- 0012-2661
- eISSN
- 1608-3083
- DOI
- 10.1134/S001226611507006X
- Publisher site
- See Article on Publisher Site
Abstract
We consider a parabolic equation whose spatial operator depends nonlinearly not only on the unknown function and its gradient but also on a nonlocal (integral) characteristic of the solution. By using the semidiscretization method with respect to the variable t and the finite element method in the space variables, we construct an approximate solution method in which the nonlocality is pulled down to the lower layer. We prove a theorem on the convergence of the constructed algorithm under minimal assumptions on the smoothness of the original data.
Journal
Differential Equations – Springer Journals
Published: Aug 13, 2015