On some statements of nonlinear parabolic problems with boundary conditions of the first kind and on methods of their approximate solution

Authors

DOI:

https://doi.org/10.26089/NumMet.v19r429

Keywords:

parabolic equations, boundary value problem of the first kind, Hölder spaces, Rothe method, inverse problems, final observation, stability estimates, quasisolutions

Abstract

We study two statements of nonlinear problems in H"{o}lder spaces for a parabolic equation with an unknown coefficient at the time derivative and with boundary conditions of the first kind. One statement is a system containing a boundary value problem and an equation for the time dependence of the sought coefficient. In the other statement, in addition it is necessary to determine a boundary function in one of the boundary conditions by using an additional information on this coefficient at a final time. For these statements we justify a construction of approximate solutions on the basis of the Rothe method and the method of quasisolutions.

Author Biography

N.L. Gol’dman

Lomonosov Moscow State University,
Research Computing Center,
Ленинские горы, 119991, Москва
• Leading Researcher

References

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Published

24-12-2018

How to Cite

Гольдман Н.Л. On Some Statements of Nonlinear Parabolic Problems With Boundary Conditions of the First Kind and on Methods of Their Approximate Solution // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2018. 19. 314-326. doi 10.26089/NumMet.v19r429

Issue

Section

Section 1. Numerical methods and applications

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