A remark on positively invariant regions for parabolic systems with an application arising in superconductivity
Authors:
Nicholas D. Alikakos and Daniel Phillips
Journal:
Quart. Appl. Math. 45 (1987), 75-80
MSC:
Primary 35K55; Secondary 35B35
DOI:
https://doi.org/10.1090/qam/885169
MathSciNet review:
885169
Full-text PDF Free Access
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Additional Information
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- David L. Barrow and Peter W. Bates, Bifurcation and stability of periodic traveling waves for a reaction-diffusion system, J. Differential Equations 50 (1983), no. 2, 218–233. MR 719447, DOI https://doi.org/10.1016/0022-0396%2883%2990075-X
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K. N. Chueh, C. L. Conley, and J. A. Smoller, Positively invariant regions for systems of diffusion equations, Indiana Univ. Math. J. 26, 373–391 (1977)
- Daniel Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, vol. 840, Springer-Verlag, Berlin-New York, 1981. MR 610244
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E. Abrahams and T. Tsuneto, Time variation of the Ginzberg-Landau order parameter, Phys. Rev. 152, 416–463 (1966)
N. D. Alikakos, Quantitative maximum principles and strongly coupled gradient-like reaction-diffusion systems, Proc. Royal Soc. Edinburgh Sect. A 94, 265–286 (1983)
D. L. Barrow and P. W. Bates, Bifurcation and stability of periodic travelling waves for a reaction-diffusion system, J. Differential Equations 50, 218–233 (1983)
K. J. Brown, P. C. Dunne, and R. A. Gardner, A semilinear parabolic system arising in the theory of superconductivity, J. Differential Equations 40, 232–252 (1981)
K. N. Chueh, C. L. Conley, and J. A. Smoller, Positively invariant regions for systems of diffusion equations, Indiana Univ. Math. J. 26, 373–391 (1977)
D. Henry, Geometric theory of parabolic equations, Lecture Notes in Math., vol. 840, Springer-Verlag, Berlin, 1981.
S. Lojasiewicz, Une propriété topologique des sous-ensembles analytiques réels, Colloques International x du C.N.R.S. #117, Les équations aux dérivées partielles, 1963
D. W. Nicholson, Eigenvalue bounds for AB + BA, with A, B positive definite matrices, Linear Algebra Appl. 24, 173–183 (1979)
P. H. Rabinowitz, Variational methods form linear eigenvalue problems, Course lectures, CIME, Varenna, Italy, 1974
L. Simon, Asymptotics for a class of non-linear evolution equations, with applications to geometric problems, Ann. of Math., (2) 118, 525–517 (1983)
J. Smoller, Shock waves and reaction-diffusion equations, Springer-Verlag, 1983
W. G. Strang, Eigenvalues of Jordan products, Amer. Math. Monthly, 37–40 (1982)
H. Weinberger, Invariant sets for weakly coupled parabolic and elliptic systems, Rend. Mat. (6) 8, 295–310 (1975)
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© Copyright 1987
American Mathematical Society
