MSC:
34D20,
35B35,
35K51,
35K57,
35K86,
35K87,
47H05,
47H11,
47J20,
47J35 | MR 3238834 | Zbl 06362253 | DOI: 10.21136/MB.2014.143849

Full entry |
PDF
(0.3 MB)
Feedback

reaction-diffusion system; Signorini condition; unilateral obstacle; instability; asymptotic stability; parabolic obstacle equation

References:

[1] Drábek, P., Kučera, M., Míková, M.: **Bifurcation points of reaction-diffusion systems with unilateral conditions**. Czech. Math. J. 35 (1985), 639-660. MR 0809047 | Zbl 0604.35042

[2] Eisner, J., Kučera, M., Väth, M.: **Bifurcation points for a reaction-diffusion system with two inequalities**. J. Math. Anal. Appl. 365 (2010), 176-194. DOI 10.1016/j.jmaa.2009.10.037 | MR 2585089 | Zbl 1185.35074

[3] Henry, D.: **Geometric Theory of Semilinear Parabolic Equations**. Lecture Notes in Mathematics 840 Springer, Berlin (1981). DOI 10.1007/BFb0089647 | MR 0610244 | Zbl 0456.35001

[4] Kim, I.-S., Väth, M.: **The Krasnosel'skii-Quittner formula and instability of a reaction-diffusion system with unilateral obstacles**. Submitted to Dyn. Partial Differ. Equ. 20 pages.

[5] Kučera, M., Väth, M.: **Bifurcation for a reaction-diffusion system with unilateral and {Neumann} boundary conditions**. J. Differ. Equations 252 (2012), 2951-2982. DOI 10.1016/j.jde.2011.10.016 | MR 2871789 | Zbl 1237.35013

[6] Mimura, M., Nishiura, Y., Yamaguti, M.: **Some diffusive prey and predator systems and their bifurcation problems**. Bifurcation Theory and Applications in Scientific Disciplines (Papers, Conf., New York, 1977) O. Gurel, O. E. Rössler Ann. New York Acad. Sci. 316 (1979), 490-510. DOI 10.1111/j.1749-6632.1979.tb29492.x | MR 0556853 | Zbl 0437.92027

[7] Turing, A. M.: **The chemical basis of morphogenesis**. Phil. Trans. R. Soc. London Ser. B 237 (1952), 37-72. DOI 10.1098/rstb.1952.0012

[8] Väth, M.: **Ideal Spaces**. Lecture Notes in Mathematics 1664 Springer, Berlin (1997). DOI 10.1007/BFb0093548 | MR 1463946 | Zbl 0896.46018

[9] Väth, M.: **Continuity and differentiability of multivalued superposition operators with atoms and parameters. I**. Z. Anal. Anwend. 31 (2012), 93-124. DOI 10.4171/ZAA/1450 | MR 2899873 | Zbl 1237.47065

[10] Ziemer, W. P.: **Weakly Differentiable Functions. Sobolev Spaces and Functions of Bounded Variation**. Graduate Texts in Mathematics 120 Springer, Berlin (1989). DOI 10.1007/978-1-4612-1015-3 | MR 1014685 | Zbl 0692.46022