Existence and uniqueness of a~weak solution of a~nonlocal aggregation equation with degenerate diffusion of general form
Sbornik. Mathematics, Tome 209 (2018) no. 2, pp. 206-221
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The uniqueness of a weak solution of a nonlocal aggregation equation with degenerate diffusion is proved using the method of energy estimates. The existence of a solution is proved by combining the methods of iterations and contraction maps with the use of energy estimates. The equations under consideration arise in models of biological aggregation.
Bibliography: 23 titles.
Keywords:
aggregation equation, uniqueness of a solution
Mots-clés : existence of a solution.
Mots-clés : existence of a solution.
@article{SM_2018_209_2_a3,
author = {V. F. Vil'danova},
title = {Existence and uniqueness of a~weak solution of a~nonlocal aggregation equation with degenerate diffusion of general form},
journal = {Sbornik. Mathematics},
pages = {206--221},
publisher = {mathdoc},
volume = {209},
number = {2},
year = {2018},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2018_209_2_a3/}
}
TY - JOUR AU - V. F. Vil'danova TI - Existence and uniqueness of a~weak solution of a~nonlocal aggregation equation with degenerate diffusion of general form JO - Sbornik. Mathematics PY - 2018 SP - 206 EP - 221 VL - 209 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SM_2018_209_2_a3/ LA - en ID - SM_2018_209_2_a3 ER -
%0 Journal Article %A V. F. Vil'danova %T Existence and uniqueness of a~weak solution of a~nonlocal aggregation equation with degenerate diffusion of general form %J Sbornik. Mathematics %D 2018 %P 206-221 %V 209 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/SM_2018_209_2_a3/ %G en %F SM_2018_209_2_a3
V. F. Vil'danova. Existence and uniqueness of a~weak solution of a~nonlocal aggregation equation with degenerate diffusion of general form. Sbornik. Mathematics, Tome 209 (2018) no. 2, pp. 206-221. http://geodesic.mathdoc.fr/item/SM_2018_209_2_a3/