GlobalExistenceandUniquenessoftheWeakSolutioninKellerSegelModel

Transcription

1 Global Journal of Science Frontier Research: F Mathematics and Decision Sciences Volume 14 Issue 2 Version 1.0 Year 2014 Type : Double Blind Peer Reviewed International Research Journal Publisher: Global Journals Inc. (USA Online ISSN: & Print ISSN: Global Existence and Uniqueness of the Weak Solution in Keller Segel Model By C. Messikh, A. Guesmia & S. Saadi University of Badji Moktar, Algeria Abstract- This paper deals with the global existence, uniqueness and boundedness of the weak solution for the chemotaxis system (P defined as The system (P is under homogeneous Dirichlet boundary conditions in a convex smooth bounded domain with smooth boundary Based on Galerkin s method, Lax -Milgran s and maximum principle, a prove of the existence and uniqueness of a global solution for the system (P is determined. Moreover we show that the unique solution is positive. Keywords and Phrases: chemotaxis, global existence, boundedness, positive solution. GJSFR-F Classification : MSC 2010: 35K58, 45G05, 65C35, 82C22, 82C31,82C80, 92C17 GlobalExistenceandUniquenessoftheWeakSolutioninKellerSegelModel : Strictly as per the compliance and regulations of C. Messikh, A. Guesmia & S. Saadi. This is a research/review paper, distributed under the terms of the Creative Commons Attribution-Noncommercial 3.0 Unported License permitting all non commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

2 Ref I. Global Existence and Uniqueness of the Weak Solution in Keller Segel Model C. Messikh, A. Guesmia & S. Saadi Abstract- This paper deals with the global existence, uniqueness and boundedness of the weak solution for the chemotaxis system (P defined as The system (P is under homogeneous Dirichlet boundary conditions in a convex smooth bounded domain with smooth boundary Based on Galerkin s method, Lax-Milgran s Theorem and maximum principle, a prove of the existence and uniqueness of a global solution for the system (P is determined. Moreover we show that the unique solution is positive. Keywords and Phrases: chemotaxis, global existence, boundedness, positive solution. I. Introduction Global Journal of Science Frontier Research F Volume XIV Issue II V ersion I Year Author : University of Badji Moktar, Laboratory LMA, Department of Mathematics, Faculty of Sciences, BP El Hadjer Algeria. messikhc@yahoo.fr Author : University of Skika 20 août 1955 Department of Mathematics, Faculty of Science. Guesmiasaid@yahoo.fr Author : University of Badji Moktar, Laboratory LANOS, Department of Mathematics, Faculty of Sciences, BP El Hadjer Algeria. Signor 2000@yahoo.fr

3 Global Journal of Science Frontier Research F Volume XIV Issue II V ersion I Year Ref

4 I. II. Existence of Weak Solution of the Problem (P a Existence of weak solution of the problem (P2 Global Journal of Science Frontier Research F Volume XIV Issue II V ersion I Year

5 Global Journal of Science Frontier Research F Volume XIV Issue II V ersion I Year Existence of a weak solution of the problem (P1 b

6 I. c Energy estimates Global Journal of Science Frontier Research F Volume XIV Issue II V ersion I Year

7 Global Journal of Science Frontier Research F Volume XIV Issue II V ersion I Year d Existence and uniqueness

8 I. Global Journal of Science Frontier Research F Volume XIV Issue II V ersion I Year

9 Global Journal of Science Frontier Research F Volume XIV Issue II V ersion I Year e Global solution of problem (P References Références Referencias

10 I. Global Journal of Science Frontier Research F Volume XIV Issue II V ersion I Year

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