We consider the general degenerate parabolic equation :
We suppose that the flux is continuous, is nondecreasing continuous and both functions are not necessarily Lipschitz. We prove the existence of the renormalized solution of the associated Cauchy problem for initial data and source term. We establish the uniqueness of this type of solution under a structure condition and an assumption on the modulus of continuity of . The novelty of this work is that , , , , are not Lipschitz functions and the techniques are different from those developed in the previous works.
Nous considérons l’équation parabolique dégénérée général :
Nous supposons que le flux est continu, est continue et croissante au sens large et les deux fonctions ne sont pas nécessairement lipschitziennes. Nous prouvons l’existence de solution renormalisée du problème de Cauchy associé à cette équation avec des données (terme source et condition initiale) dans . Nous établissons l’unicité de cette solution sous une condition dite de structure du type et sous une hypothèse sur le module de continuité de . La nouveauté dans le travail vient du fait que , , , , ne sont pas des fonctions nécessairement lipschitziennes et les techniques sont différentes de celles développées dans les travaux antérieurs.
@article{AFST_2008_6_17_3_597_0, author = {Maliki, Mohamed and Ouedraogo, Adama}, title = {Renormalized solution for nonlinear degenerate problems in the whole space}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {597--611}, publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques}, address = {Toulouse}, volume = {Ser. 6, 17}, number = {3}, year = {2008}, doi = {10.5802/afst.1194}, zbl = {1173.35565}, mrnumber = {2488233}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/afst.1194/} }
TY - JOUR AU - Maliki, Mohamed AU - Ouedraogo, Adama TI - Renormalized solution for nonlinear degenerate problems in the whole space JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2008 SP - 597 EP - 611 VL - 17 IS - 3 PB - Université Paul Sabatier, Institut de mathématiques PP - Toulouse UR - http://archive.numdam.org/articles/10.5802/afst.1194/ DO - 10.5802/afst.1194 LA - en ID - AFST_2008_6_17_3_597_0 ER -
%0 Journal Article %A Maliki, Mohamed %A Ouedraogo, Adama %T Renormalized solution for nonlinear degenerate problems in the whole space %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2008 %P 597-611 %V 17 %N 3 %I Université Paul Sabatier, Institut de mathématiques %C Toulouse %U http://archive.numdam.org/articles/10.5802/afst.1194/ %R 10.5802/afst.1194 %G en %F AFST_2008_6_17_3_597_0
Maliki, Mohamed; Ouedraogo, Adama. Renormalized solution for nonlinear degenerate problems in the whole space. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 17 (2008) no. 3, pp. 597-611. doi : 10.5802/afst.1194. http://archive.numdam.org/articles/10.5802/afst.1194/
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