We prove the existence, uniqueness and non-negativity of solutions for a nonlinear stationary Doi–Edwards equation. The existence is proved by a perturbation argument. We get the uniqueness and the non-negativity by showing the convergence in time of the solution of the evolutionary Doi–Edwards equation towards any stationary solution.
@article{AIHPC_2016__33_5_1353_0, author = {Ciuperca, Ionel Sorin and Heibig, Arnaud}, title = {Existence and uniqueness of a density probability solution for the stationary {Doi{\textendash}Edwards} equation}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {1353--1373}, publisher = {Elsevier}, volume = {33}, number = {5}, year = {2016}, doi = {10.1016/j.anihpc.2015.05.003}, zbl = {1356.35254}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2015.05.003/} }
TY - JOUR AU - Ciuperca, Ionel Sorin AU - Heibig, Arnaud TI - Existence and uniqueness of a density probability solution for the stationary Doi–Edwards equation JO - Annales de l'I.H.P. Analyse non linéaire PY - 2016 SP - 1353 EP - 1373 VL - 33 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2015.05.003/ DO - 10.1016/j.anihpc.2015.05.003 LA - en ID - AIHPC_2016__33_5_1353_0 ER -
%0 Journal Article %A Ciuperca, Ionel Sorin %A Heibig, Arnaud %T Existence and uniqueness of a density probability solution for the stationary Doi–Edwards equation %J Annales de l'I.H.P. Analyse non linéaire %D 2016 %P 1353-1373 %V 33 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2015.05.003/ %R 10.1016/j.anihpc.2015.05.003 %G en %F AIHPC_2016__33_5_1353_0
Ciuperca, Ionel Sorin; Heibig, Arnaud. Existence and uniqueness of a density probability solution for the stationary Doi–Edwards equation. Annales de l'I.H.P. Analyse non linéaire, Volume 33 (2016) no. 5, pp. 1353-1373. doi : 10.1016/j.anihpc.2015.05.003. http://www.numdam.org/articles/10.1016/j.anihpc.2015.05.003/
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