Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (1983), pp. 20-24
Citer cet article
A. S. Kalashnikov. The heat equation in a medium with nonuniformly distributed nonlinear heat sources or absorbers. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (1983), pp. 20-24. http://geodesic.mathdoc.fr/item/VMUMM_1983_3_a3/
@article{VMUMM_1983_3_a3,
author = {A. S. Kalashnikov},
title = {The heat equation in a medium with nonuniformly distributed nonlinear heat sources or absorbers},
journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
pages = {20--24},
year = {1983},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMUMM_1983_3_a3/}
}
TY - JOUR
AU - A. S. Kalashnikov
TI - The heat equation in a medium with nonuniformly distributed nonlinear heat sources or absorbers
JO - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY - 1983
SP - 20
EP - 24
IS - 3
UR - http://geodesic.mathdoc.fr/item/VMUMM_1983_3_a3/
LA - ru
ID - VMUMM_1983_3_a3
ER -
%0 Journal Article
%A A. S. Kalashnikov
%T The heat equation in a medium with nonuniformly distributed nonlinear heat sources or absorbers
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 1983
%P 20-24
%N 3
%U http://geodesic.mathdoc.fr/item/VMUMM_1983_3_a3/
%G ru
%F VMUMM_1983_3_a3
For a heat conduction equation with non-linear sources whose action intensifies at infinity, it is proved that the Cauchy problem has no locally bounded solution in any time interval. In the case of non-linear heat absorption decaying at infinity, necessary and sufficient conditions are found for instantaneous compactification of the support of the solution for the Cauchy problem.
