Geodesic
A nonlinear problem for a parabolic equation with an unknown coefficient at the time derivative and its applications in mathematical models of physico-chemical processes
Numerical methods and programming, Tome 18 (2017) no. 3, pp. 247-266 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider conditions of unique solvability in a class of smooth functions for a nonlinear system with an unknown coefficient at the time derivative in a parabolic equation. To this end, the Rothe method is applied, which provides not only the proof of solvability but also the constructive solution of the considered system. A priori estimates in the grid-continuous Hölder spaces are established for the corresponding differential-difference nonlinear system that approximates the initial parabolic system by the Rothe method. Such estimates allow one to prove the existence of the smooth solution of this parabolic system and to obtain the error estimates for the Rothe method. This study is connected with the mathematical modelling of physico-chemical processes where the inner characteristics of materials are subjected to changes. As an example, the problem on the destruction of a heat-protective composite under the effect of high-temperature heating is discussed.
Mots-clés : parabolic equations, Hölder spaces
Keywords: Rothe method, a priori estimates, unique solvability, mathematical model, thermodestruction, composite material. 
@article{VMP_2017_18_3_a5,
     author = {N. L. Gol'dman},
     title = {A nonlinear problem for a parabolic equation with an unknown coefficient at the time derivative and its applications in mathematical models of physico-chemical processes},
     journal = {Numerical methods and programming},
     pages = {247--266},
     year = {2017},
     volume = {18},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2017_18_3_a5/}
}
TY  - JOUR
AU  - N. L. Gol'dman
TI  - A nonlinear problem for a parabolic equation with an unknown coefficient at the time derivative and its applications in mathematical models of physico-chemical processes
JO  - Numerical methods and programming
PY  - 2017
SP  - 247
EP  - 266
VL  - 18
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VMP_2017_18_3_a5/
LA  - ru
ID  - VMP_2017_18_3_a5
ER  - 
%0 Journal Article
%A N. L. Gol'dman
%T A nonlinear problem for a parabolic equation with an unknown coefficient at the time derivative and its applications in mathematical models of physico-chemical processes
%J Numerical methods and programming
%D 2017
%P 247-266
%V 18
%N 3
%U http://geodesic.mathdoc.fr/item/VMP_2017_18_3_a5/
%G ru
%F VMP_2017_18_3_a5
N. L. Gol'dman. A nonlinear problem for a parabolic equation with an unknown coefficient at the time derivative and its applications in mathematical models of physico-chemical processes. Numerical methods and programming, Tome 18 (2017) no. 3, pp. 247-266. http://geodesic.mathdoc.fr/item/VMP_2017_18_3_a5/