A qualitative theory for parabolic problems under dynamical boundary conditions

Journal of Inequalities and Applications

Volumn 5, Issue 5, 2000, Pages 467-486

  Von Below, Joachim ^a   De Coster, Colette ^a  

^a UNIVERSITÉ DU LITTORAL CÔTE D OPALE   (France)

Author keywords

Convergence to equilibria; Dynamical boundary conditions; Maximum and comparison principles; Parabolic problems; Upper and lower solutions

Indexed keywords

EID: 0037909853     PISSN: 10255834     EISSN: 1029242X     Source Type: Journal    
DOI: 10.1155/S1025583400000266     Document Type: Article

References (11)

1. H. Amann, Ordinary Differential Equations, Walter de Gruyter, Berlin 1990.
2. J. von Below, A Maximum Principle for Semilinear Parabolic Network Equations, in, J. A. Goldstein, F. Kappel and W. Schappacher (Eds.), Differential equations with applications in biology, physics, and engineering, Lect. Not. Pure Appl. Math. Vol. 133, M. Dekker Inc., New York, 1991, pp. 37-45.
3. J. von Below, An Existence Result for Semilinear Parabolic Network Equations with Dynamical Node Conditions, in, C. Bandle, J. Bemelmans, M. Chipot, M. Grüter and J. Saint Jean Paulin (Eds.), Progress in partial differential equations: elliptic and parabolic problems, Pitman Research Notes in Math. Ser. Vol. 266. Longman Harlow Essex, 1992, pp. 274-283.
4. J. von Below, Parabolic Network Equations, 3rd edn. (to appear).
5. J. von Below, A Maximum Principle for Fully Nonlinear Parabolic Equations with Time Degeneracy, Cahiers LMPA Liouville ULCO No. 95 (1999) (to appear).
6. J. von Below and S. Nicaise, Dynamical Interface Transition in Ramified Media with Diffusion, Comm. Partial Differential Equations, 21(1996), 255-279.
7. C. De Coster and P. Omari, Unstable Periodic Solutions for a Parabolic Problem in Presence of Non-well-ordered Lower and Upper Solutions, Cahiers LMPA Liouville ULCO No. 101 (1999) (submitted).
8. T. Hintermann, Evolution Equations with Dynamic Boundary Conditions, Proc. Royal Soc. Edinburgh, 113 A (1989), 43-60.
9. O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Uraltseva, Linear and Quasilinear Equations of Parabolic Type, Trans. Math. Monographs 23, A. M. S., Providence, R. I. (1968).
10. M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, 1967.
11. W. Walter, Differential and Integral Inequalities, Springer Verlag, Berlin, 1970.