| Title:
|
Reaction-diffusion systems: stabilizing effect of conditions described by quasivariational inequalities (English) |
| Author:
|
Kučera, Milan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
47 |
| Issue:
|
3 |
| Year:
|
1997 |
| Pages:
|
469-486 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Reaction-diffusion systems are studied under the assumptions guaranteeing diffusion driven instability and arising of spatial patterns. A stabilizing influence of unilateral conditions given by quasivariational inequalities to this effect is described. (English) |
| Keyword:
|
reaction-diffusion systems |
| Keyword:
|
unilateral conditions |
| Keyword:
|
bifurcation |
| Keyword:
|
quasivariational inequalities |
| Keyword:
|
spatial patterns |
| MSC:
|
35B32 |
| MSC:
|
35B35 |
| MSC:
|
35J85 |
| MSC:
|
35K57 |
| MSC:
|
47A75 |
| MSC:
|
92D25 |
| idZBL:
|
Zbl 0898.35010 |
| idMR:
|
MR1461426 |
| . |
| Date available:
|
2009-09-24T10:07:28Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127371 |
| . |
| Reference:
|
[1] P. Drábek, M. Kučera and M. Míková: Bifurcation points of reaction-diffusion systems with unilateral conditions.Czechoslovak Math. J. 35 (1985), 639–660. MR 0809047 |
| Reference:
|
[2] P. Drábek, M. Kučera: Eigenvalues of inequalities of reaction-difusion type and destabilizing effect of unilateral conditions.Czechoslovak Math. J. 36 (1986), 116–130. MR 0822872 |
| Reference:
|
[3] P. Drábek, M. Kučera: Reaction-diffusion systems: Destabilizing effect of unilateral conditions.Nonlinear Analysis, Theory, Methods, Applications 12 (1988), 1173–1192. MR 0969497 |
| Reference:
|
[4] S. Fučík and A. Kufner: Nonlinear Differential Equations.Elsevier, Amsterdam, 1980. MR 0558764 |
| Reference:
|
[5] M. Kučera: Stability and bifurcation problems for reaction-diffusion system with unilateral conditions.Equadiff 6, Vosmanský, J. – Zlámal, M. (eds.), Brno, Universita J. E. Purkyně, 1986, pp. 227–234. MR 0877129 |
| Reference:
|
[6] M. Kučera, M. Bosák: Bifurcation for quasi-variational inequalities of reaction-diffusion type.Stability and Applied Analysis of Continuous Media, Pitagora, Bologna, Vol. 3, No. 2, 1993, pp. 111–127. |
| Reference:
|
[7] M. Kučera: Bifurcation of solutions to reaction-diffusion system with unilateral conditions.Navier-Stokes Equations and Related Nonlinear Problems, A. Sequeira (ed.), Plenum Press, New York, 1995, pp. 307–322. MR 1373224 |
| Reference:
|
[8] M. Kučera: Reaction-diffusion systems: Bifurcation and stabilizing effect of unilateral conditions given by inclusions.Nonlin. Anal., T. M. A. 27 (1996), no. 3, 249–260. MR 1391435, 10.1016/0362-546X(95)00055-Z |
| Reference:
|
[9] J.L. Lions, E. Magenes: Problèmes aux limits non homogènes.Dunod, Paris, 1968. |
| Reference:
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[10] M. Mimura, Y. Nishiura and M. Yamaguti: Some diffusive prey and predator systems and their bifurcation problems.Ann. N.Y. Acad. Sci. 316 (1979), 490–521. MR 0556853, 10.1111/j.1749-6632.1979.tb29492.x |
| Reference:
|
[11] U. Mosco: Implicit variational problems and quasi variational inequalities.Nonlinear Operators and the calculus of Variations (Summer School, Univ. Libre Bruxelles, Brussels), Lecture Notes in Math., Vol. 543, Springer Berlin, pp. 83–156. Zbl 0346.49003, MR 0513202 |
| Reference:
|
[12] Y. Nishiura: Global structure of bifurcating solutions of some reaction-diffusion systems.SIAM J. Math. Analysis 13 (1982), 555–593. Zbl 0505.76103, MR 0661590, 10.1137/0513037 |
| Reference:
|
[13] P. Quittner: Bifurcation points and eigenvalues of inequalities of reaction-diffusion type.J. reine angew. Math. 380 (1987), 1–13. Zbl 0617.35053, MR 0916198 |
| Reference:
|
[14] D. H. Sattinger: Topics in Stability and Bifurcation Theory.Lecture Notes in Mathematics 309, Springer-Verlag, Berlin-Heidelberg-New York, 1973. Zbl 0248.35003, MR 0463624 |
| Reference:
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[15] E. Zarantonello: Projections on convex sets in Hilbert space and spectral theory.Contributions to Nonlinear Functional Analysis, E. H. Zarantonello (ed.), Academic Press, New York, 1971. Zbl 0281.47043 |
| . |
