×

Remarks on invariance in reaction-diffusion equations. (English) Zbl 0463.35044


MSC:

35K55 Nonlinear parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
35B50 Maximum principles in context of PDEs
35B35 Stability in context of PDEs
35B45 A priori estimates in context of PDEs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Alikakos, N. D., An application of the invariance principle to reaction-diffusion equations, J. diff. Eqns., 39 (1979) · Zbl 0386.34046
[2] Casten, R. G.; Holland, C. S., Stability properties of solutions to systems of reaction-diffusion equations, SIAM J. appl. Math, 33 (1977) · Zbl 0372.35044
[3] Chueh, K. N.; Conley, C. C.; Smoller, J. A., Positively invariant regions for systems of diffusion equations, I.U.M.J., 26 (1977) · Zbl 0368.35040
[5] Conway, E. D.; Smoller, J. A., Nonlinear diffusion, Research Notes in Math, No. 14 (1977), Pitman · Zbl 0359.35040
[6] Conway, E. D.; Smoller, J. A., Diffusion and the predator-prey interaction, SIAM J. appl. Math., 33 (1977) · Zbl 0359.35040
[8] Friedman, A., Partial Differential Equations (1969), Holt, Rinehart and Winston: Holt, Rinehart and Winston New York · Zbl 0224.35002
[9] Hale, J. K., Dynamical systems and stability, J. math. Aud. Appl., 26 (1969) · Zbl 0179.13303
[10] Hastings, A., Global stability in Lotka-Volterra systems with diffusion, J. math. Biol. (1978) · Zbl 0393.92013
[12] Glushko, V. P.; Krein, S. G., Fractional powers of differential operators and embedding theorems, Pokl. Acad. Nauk. SSSR, 122, 963-966 (1958) · Zbl 0089.32503
[13] LaSalle, J. P., Stability theory and the asymptotic behaviour of dynamical systems, (Dynamic Stability and Structures, Proc. Int. Conf. (1966), Pergamon: Pergamon Long Island City, New York) · Zbl 0153.40602
[14] Nicholson, D. W., Eigenvalue bounds for AB+BA, with \(A, B\) positive definite matrices, Linear Algebra and Appl., 24 (1979) · Zbl 0404.15006
[15] Pazy, A., Semigroups and Applications to Partial Differential Equations (1974), Univ. of Maryland Press · Zbl 0516.47023
[16] Rauch, J.; Smoller, J., Qualitative theory of the Fitzhugh-Nagumo equation, Adv. Math., 21, 12-44 (1978) · Zbl 0379.92002
[17] Weinberger, H., Invariant sets for weakly coupled parabolic and elliptic systems, Rend. Mat. Univ. Roma, 8 (1975) · Zbl 0312.35043
[18] Williams, S.; Chow, P. L., Nonlinear reaction-diffusion models, J. math. Analysis Applic., 62 (1978) · Zbl 0372.35047
[19] Noble, B.; Daniel, J. W., Applied Linear Algebra (1977), Prentice Hall: Prentice Hall New York · Zbl 0413.15002
[20] Othmer, H. G., Synchronized and differentiated modes of cellular dynamics, (Haken, H., Dynamics of Synergetic Systems (1980), Springer-Verlag: Springer-Verlag Berlin), (Edited by H. Haken) · Zbl 0433.92004
[21] Conway, E. D.; Hoff, D.; Smoller, J. A., Large time behavior of solutions of systems of nonlinear reaction-diffusion equations, SIAM J. Appl. Math., 35 (1978) · Zbl 0383.35035
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.