Proceedings of the American Mathematical Society

Author(s): C. V. Pao
Journal: Proc. Amer. Math. Soc. 130 (2002), 1079-1086.
MSC (1991): Primary 35K50; Secondary 35K57
Posted: September 14, 2001
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Abstract: The aim of this paper is to show the existence and uniqueness of a solution for a system of time-delayed parabolic equations with coupled nonlinear boundary conditions. The time delays are of discrete type which may appear in the reaction function as well as in the boundary function. The approach to the problem is by the method of upper and lower solutions for nonquasimonotone functions.

1.: J. M. Cushing, Integrodifferential Equations and Delay Models in Population Dynamics, Lecture Notes in Biomath., Vol. 20, Springer-Verlag, New York, 1977. MR 58:15300
2.: W. E. Fitzgibbon, Semilinear functional differential equations in Banach space, J. Differential Equations, 29 (1978), 1-14. MR 58:11746
3.: A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, NJ, 1964. MR 31:6062
4.: X. Lu, Persistence and extinction in a competition-diffusion system with time delays, Canadian Appl. Math. Quart., 2 (1994), 231-246. MR 95e:92016
5.: S. Luckhaus, Global boundedness for a delay differential equation, Trans. Amer. Math. Soc., 294 (1986), 767-774. MR 87j:35053
6.: J. M. Mahaffy and C. V. Pao, Models of genetic control by repression with time delays and spatial effects, J. Math. Biol., 20 (1984), 39-57. MR 85h:92011
7.: R. H. Martin and H. L. Smith, Abstract functional differential equations and reaction diffusion systems, Trans. Amer. Math. Soc., 321 (1990), 1-44. MR 90m:35194
8.: C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum, New York, 1992. MR 94c:35002
9.: C. V. Pao, Coupled nonlinear parabolic systems with time delays, J. Math. Anal. Appl., 196 (1995), 237-265. MR 96j:35260
10.: C. V. Pao, Systems of parabolic equations with continuous and discrete delays, J. Math. Anal. Appl., 205 (1997), 157-185. MR 97j:35155
11.: C. V. Pao, On a coupled reaction diffusion system with time delays, SIAM J. Math. Anal., 18 (1987), 1026-1039. MR 88d:35105
12.: S. M. Rankin, Existence and asymptotic behavior of a functional differential equation in Banach space, J. Math. Anal. Appl., 88 (1982), 531-542. MR 84h:35160
13.: R. Redlinger, Existence theorems for semilinear parabolic systems with functionals, Nonlinear Analysis, TMA, 8 (1984), 667-682. MR 86a:35080
14.: C. C. Travis and G. F. Webb, Existence and stability for partial functional differential equations, Trans. Amer. Math. Soc., 200 (1974), 395-418. MR 52:3690
15.: J. Wu, Theory and Applications of Partial Functional Differential Equations, Springer-Verlag, New York, 1996. MR 98a:35135

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 35K50, 35K57

C. V. Pao
Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205
Email: cvpao@math.ncsu.edu

DOI: 10.1090/S0002-9939-01-06319-5
PII: S 0002-9939(01)06319-5
Keywords: Parabolic systems, time delays, nonlinear boundary conditions, existence-uniqueness, nonquasimonotone functions, upper and lower solutions
Received by editor(s): October 5, 2000
Posted: September 14, 2001
Communicated by: David S. Tartakoff
Copyright of article: Copyright 2001, American Mathematical Society

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