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


  • N.L. Gol’dman


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


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.





Section 1. Numerical methods and applications

Author Biography

N.L. Gol’dman

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


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