The Cauchy problem for a coupled semilinear parabolic system

Nonlinear Analysis, Theory, Methods and Applications

Volumn 52, Issue 3, 2002, Pages 891-904

  Amour, L ^a   Raoux, T ^a  

^a UNIVERSITÉ DE REIMS CHAMPAGNE ARDENNE   (France)

Author keywords

Global existence; Invariant sets; Nonlinear gradients terms; Nonlinear parabolic systems

Indexed keywords

FUNCTION EVALUATION; GRADIENT METHODS; INTEGRAL EQUATIONS; PROBLEM SOLVING; SET THEORY;

PARABOLIC SYSTEMS;

NONLINEAR SYSTEMS;

EID: 0037210256     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(02)00139-6     Document Type: Article

References (14)

1. Amann H. Invariant sets and existence theorems for semilinear parabolic and elliptic systems. J. Math. Anal. Appl. 65:1978;432-467.
2. Amour L., Ben-Artzi M. Global existence and decay for viscous Hamilton-Jacobi equations. Nonlinear Anal. TMA. 31:1998;621-628.
3. 1 des solutions d'un système parabolique semi-linéaire C. R. Acad. Sci. Paris Sér. I. 329(5):1999;367-370.
4. 1 decay properties for a semilinear parabolic system Israel J. Math. 123:2001;157-177.
5. Bates P.W. Containment for weakly parabolic systems. Houston J. Math. 11:1985;151-158.
6. Benachour S., Laurençot P. Global solutions to viscous Hamilton-Jacobi equations with irregular initial data. Comm. Partial Differential Equations. 24(11-12):1999;1999-2021.
7. Ben-Artzi M., Souplet P., Weissler F.B. Sur la non-existence et la non-unicité des solutions du problème de Cauchy pour une équation parabolique semi-linéaire. C. R. Acad. Sci. Paris Sér. I. 329(5):1999;371-376.
8. Cosner C., Schaefer P.W. On the development of functionals which satisfy a Maximum principle. Appl. Anal. 26:1987;45-60.
9. Krezin G.I., Maz'ya V.G. Criteria for validity of the maximum modulus principle for solutions of linear parabolic systems. Ark. Mat. 32(1):1994;121-155.
10. Ladyženskaja O.A., Solonnikov V.A., Ural'ceva N.N. Linear and quasilinear equations of parabolic type. Translations of Mathematical Monographs. Vol. 23:1968;American Mathematical Society, Providence, RI.
11. P. Laurençot, Decay of mass for a semilinear parabolic system: the critical case, preprint, 2001.
12. Protter M., Weinberger H. Maximum Principles in Differential Equations. 1967;Prentice-Hall, Englewood Cliffs, NJ.
13. Redheffer R., Walter W. Invariant sets for systems of partial differential equations, I. Parabolic equations. Arch. Rational Mech. Anal. 67(11-12):1977;41-52.
14. Weinberger H. Invariant sets for weakly coupled parabolic and elliptic systems. Rend. Mat. Ser. VI. 8(8):1975;295-310.