Geodesic
Heat equation with degeneration in Holder and Slobodetskii spaces
Matematičeskie zametki, Tome 58 (1995) no. 2, pp. 189-203

Voir la notice de l'article provenant de la source Math-Net.Ru

We study initial-boundary value problems for the heat equation in which heat conductivity $\alpha^2(x)$ may depend on the space variable $x\in\mathbb R^+$; the nonnegative function $\alpha(x)$ is allowed to tend to infinity (respectively, zero) as $x\to+\infty$ (respectively, $x\to+0$). We prove that these problems are well posed and examine the smoothness of solutions. It is shown that criteria for smoothness of the solutions can be stated in terms of certain functionals, namely, the Hölder constant (for Hölder spaces) and the generalized Hölder constant (for Slobodetskii spaces). 
@article{MZM_1995_58_2_a2,
     author = {V. P. Glushko and S. A. Tkacheva},
     title = {Heat equation with degeneration in {Holder} and {Slobodetskii} spaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {189--203},
     publisher = {mathdoc},
     volume = {58},
     number = {2},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1995_58_2_a2/}
}
TY  - JOUR
AU  - V. P. Glushko
AU  - S. A. Tkacheva
TI  - Heat equation with degeneration in Holder and Slobodetskii spaces
JO  - Matematičeskie zametki
PY  - 1995
SP  - 189
EP  - 203
VL  - 58
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1995_58_2_a2/
LA  - ru
ID  - MZM_1995_58_2_a2
ER  - 
%0 Journal Article
%A V. P. Glushko
%A S. A. Tkacheva
%T Heat equation with degeneration in Holder and Slobodetskii spaces
%J Matematičeskie zametki
%D 1995
%P 189-203
%V 58
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1995_58_2_a2/
%G ru
%F MZM_1995_58_2_a2
V. P. Glushko; S. A. Tkacheva. Heat equation with degeneration in Holder and Slobodetskii spaces. Matematičeskie zametki, Tome 58 (1995) no. 2, pp. 189-203. http://geodesic.mathdoc.fr/item/MZM_1995_58_2_a2/