Geodesic
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, Tome 19 (2018) no. 4, pp. 314-326 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study two statements of nonlinear problems in Hölder 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.
Mots-clés : parabolic equations, Hölder spaces, final observation
Keywords: boundary value problem of the first kind, Rothe method, inverse problems, stability estimates, quasisolutions. 
@article{VMP_2018_19_4_a0,
     author = {N. L. Gol'dman},
     title = {On some statements of nonlinear parabolic problems with boundary conditions of the first kind and on methods of their approximate solution},
     journal = {Numerical methods and programming},
     pages = {314--326},
     year = {2018},
     volume = {19},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2018_19_4_a0/}
}
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N. L. Gol'dman. 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, Tome 19 (2018) no. 4, pp. 314-326. http://geodesic.mathdoc.fr/item/VMP_2018_19_4_a0/