Spatial decay estimates for reaction-diffusion systems
Authors:
W. E. Fitzgibbon, J. J. Morgan and L. T. Wheeler
Journal:
Quart. Appl. Math. 47 (1989), 529-538
MSC:
Primary 35K57; Secondary 35B40
DOI:
https://doi.org/10.1090/qam/1012275
MathSciNet review:
MR1012275
Full-text PDF Free Access
References |
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Additional Information
- P. W. Bates, Containment for weakly coupled parabolic systems, Houston J. Math. 11 (1985), no. 2, 151–158. MR 792191
- K. N. Chueh, C. C. Conley, and J. A. Smoller, Positively invariant regions for systems of nonlinear diffusion equations, Indiana Univ. Math. J. 26 (1977), no. 2, 373–392. MR 430536, DOI https://doi.org/10.1512/iumj.1977.26.26029
- W. E. Fitzgibbon and J. Morgan, Existence of solutions for a class of weakly coupled semilinear elliptic systems, J. Differential Equations 77 (1989), no. 2, 351–368. MR 983299, DOI https://doi.org/10.1016/0022-0396%2889%2990148-4
- W. E. Fitzgibbon and J. Morgan, Steady state solutions for certain reaction diffusion systems, Nonlinear Anal. 15 (1990), no. 1, 27–37. MR 1058768, DOI https://doi.org/10.1016/0362-546X%2890%2990012-6
W. E. Fitzgibbon, J. J. Morgan, and S. J. Waggoner, Global existence of solutions to a class of reaction diffusion systems, to appear
W. E. Fitzgibbon, J. J. Morgan, and S. J. Waggoner, Stationary solutions to a class of nonlinear reaction diffusion systems, preprint
- Cornelius O. Horgan and James K. Knowles, Recent developments concerning Saint-Venant’s principle, Adv. in Appl. Mech. 23 (1983), 179–269. MR 889288
- C. O. Horgan, L. E. Payne, and L. T. Wheeler, Spatial decay estimates in transient heat conduction, Quart. Appl. Math. 42 (1984), no. 1, 119–127. MR 736512, DOI https://doi.org/10.1090/S0033-569X-1984-0736512-8
- Cornelius O. Horgan and Lewis T. Wheeler, Spatial decay estimates for the heat equation via the maximum principle, Z. Angew. Math. Phys. 27 (1976), no. 3, 371–376 (English, with French summary). MR 441098, DOI https://doi.org/10.1007/BF01590509
J. N. Knowles, On the spatial decay of solutions of parabolic equations, Z. Angew. Math. Phys. 22, 1078–1081 (1971)
- Jeff Morgan, Global existence for semilinear parabolic systems, SIAM J. Math. Anal. 20 (1989), no. 5, 1128–1144. MR 1009350, DOI https://doi.org/10.1137/0520075
- James Serrin, A remark on the preceding paper of Herbert Amann: “A uniqueness theorem for nonlinear elliptic boundary value problems” (Arch. Rational Mech. Anal. 44 (1971/72), 178–181), Arch. Rational Mech. Anal. 44 (1971/72), 182–186. MR 410080, DOI https://doi.org/10.1007/BF00250777
J. A. Vatsano, J. E. Pearson, W. Horsthemke, and H. L. Swinney, Chemical pattern formation with equal diffusion constants, Physica D, to appear
- Hans F. Weinberger, Invariant sets for weakly coupled parabolic and elliptic systems, Rend. Mat. (6) 8 (1975), 295–310 (English, with Italian summary). MR 397126
P. Bates, Containment for weakly coupled parabolic systems, Houston J. Math. 11, 151–158 (1985)
C. Cheuh, C. Conley, and J. Smoller, Positively invariant regions for systems of nonlinear diffusion equations, Indiana Univ. Math. J. 26, 373–392 (1977)
W. E. Fitzgibbon and J. J. Morgan, Existence of solutions for a class of weakly coupled semilinear elliptic systems, J. Differential Equations 77, 351–368 (1989)
W. E. Fitzgibbon and J. J. Morgan, Steady state solutions for certain reaction diffusion systems, preprint
W. E. Fitzgibbon, J. J. Morgan, and S. J. Waggoner, Global existence of solutions to a class of reaction diffusion systems, to appear
W. E. Fitzgibbon, J. J. Morgan, and S. J. Waggoner, Stationary solutions to a class of nonlinear reaction diffusion systems, preprint
C. O. Horgan and J. K. Knowles, Recent developments concerning Saint-Venant’s principle, Adv. in Appl. Mech. 23, 179–267 (1983)
C. O. Horgan, L. E. Payne, and L. T. Wheeler, Spatial decay estimates in transient heat conduction, Quart. Appl. Math. 42, 119–127 (1984)
C. O. Horgan, and L. T. Wheeler, Spatial decay estimates for the heat equation via the maximum principle, Z. Angew. Math. Phys. 27, 371–376 (1976)
J. N. Knowles, On the spatial decay of solutions of parabolic equations, Z. Angew. Math. Phys. 22, 1078–1081 (1971)
J. J. Morgan, Global existence for semilinear parabolic systems, SIAM J. Math. Anal., to appear
J. Serrin, A Remark on the Preceding Paper of Amann, Arch. Rational Mech. Anal. 44, 182–186 (1972)
J. A. Vatsano, J. E. Pearson, W. Horsthemke, and H. L. Swinney, Chemical pattern formation with equal diffusion constants, Physica D, to appear
H. F. Weinberger, Invariant sets for weakly coupled parabolic and elliptic systems, Rendiconti di Mathematica 8 A, 295–310 (1975)
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Article copyright:
© Copyright 1989
American Mathematical Society