Blow-up boundary regimes for general quasilinear parabolic equations in multidimensional domains
Sbornik. Mathematics, Tome 190 (1999) no. 3, pp. 447-479
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A new approach (not based on the techniques of barriers) to the study of asymptotic properties of the generalized solutions of parabolic initial boundary-value problems with finite-time blow-up of the boundary values is proposed. Precise conditions on the blow-up pattern are found that guarantee uniform localization of the solution for an arbitrary compactly supported initial function. The main result of the paper consists in obtaining precise sufficient conditions for the singular (or blow-up) set of an arbitrary solution to remain within the boundary of the domain.
@article{SM_1999_190_3_a4,
author = {A. E. Shishkov and A. G. Shchelkov},
title = {Blow-up boundary regimes for general quasilinear parabolic equations in multidimensional domains},
journal = {Sbornik. Mathematics},
pages = {447--479},
publisher = {mathdoc},
volume = {190},
number = {3},
year = {1999},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1999_190_3_a4/}
}
TY - JOUR AU - A. E. Shishkov AU - A. G. Shchelkov TI - Blow-up boundary regimes for general quasilinear parabolic equations in multidimensional domains JO - Sbornik. Mathematics PY - 1999 SP - 447 EP - 479 VL - 190 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SM_1999_190_3_a4/ LA - en ID - SM_1999_190_3_a4 ER -
%0 Journal Article %A A. E. Shishkov %A A. G. Shchelkov %T Blow-up boundary regimes for general quasilinear parabolic equations in multidimensional domains %J Sbornik. Mathematics %D 1999 %P 447-479 %V 190 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/SM_1999_190_3_a4/ %G en %F SM_1999_190_3_a4
A. E. Shishkov; A. G. Shchelkov. Blow-up boundary regimes for general quasilinear parabolic equations in multidimensional domains. Sbornik. Mathematics, Tome 190 (1999) no. 3, pp. 447-479. http://geodesic.mathdoc.fr/item/SM_1999_190_3_a4/