THE GIERER & MEINHARDT SYSTEM: THE BREAKING OF HOMOCLINICS AND MULTI-BUMP GROUND STATES

作者: MANUEL del PINO , MICHAŁ KOWALCZYK , XINFU CHEN

DOI: 10.1142/S0219199701000433

关键词:

摘要: In this paper we study ground-states of the Gierer & Meinhardt system on line, namely solutions problem We prove that given any number N, there exists a solution to exhibiting exactly Nbumps in its u-component, separated from each other at distance O(|log σ|), whenever σ is sufficiently small. These bumps resemble shape unique

参考文章(11)
Izumi Takagi, Point-condensation for a reaction-diffusion system Journal of Differential Equations. ,vol. 61, pp. 208- 249 ,(1986) , 10.1016/0022-0396(86)90119-1
C-S Lin, W-M Ni, Izumi Takagi, None, Large amplitude stationary solutions to a chemotaxis system Journal of Differential Equations. ,vol. 72, pp. 1- 27 ,(1988) , 10.1016/0022-0396(88)90147-7
Wei-Ming Ni, Izumi Takagi, On the Neumann problem for some semilinear elliptic equations and systems of activator-inhibitor type Transactions of the American Mathematical Society. ,vol. 297, pp. 351- 368 ,(1986) , 10.1090/S0002-9947-1986-0849484-2
Nicholas D. Alikakos, Giorgio Fusco, Slow dynamics for the cahn-hilliard equation in higher space dimension part i: spectral estimates ∗ Communications in Partial Differential Equations. ,vol. 19, pp. 1397- 1447 ,(1994) , 10.1080/03605309408821059
Andreas Floer, Alan Weinstein, Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential Journal of Functional Analysis. ,vol. 69, pp. 397- 408 ,(1986) , 10.1016/0022-1236(86)90096-0
Nicholas D. Alikakos, Giorgio Fusco, Slow Dynamics for the Cahn‐Hilliard Equation in Higher Space Dimensions: The Motion of Bubbles Archive for Rational Mechanics and Analysis. ,vol. 141, pp. 1- 61 ,(1998) , 10.1007/S002050050072
Wei-Ming Ni, Izumi Takagi, On the shape of least‐energy solutions to a semilinear Neumann problem Communications on Pure and Applied Mathematics. ,vol. 44, pp. 819- 851 ,(1991) , 10.1002/CPA.3160440705
Juncheng Wei, Matthias Winter, On the two-dimensional Gierer-Meinhardt system with strong coupling Siam Journal on Mathematical Analysis. ,vol. 30, pp. 1241- 1263 ,(1999) , 10.1137/S0036141098347237
B. Helffer, J. Sjostrand, Multiple wells in the semi-classical limit I Communications in Partial Differential Equations. ,vol. 9, pp. 337- 408 ,(1984) , 10.1080/03605308408820335
A. Gierer, H. Meinhardt, A theory of biological pattern formation. Kybernetika. ,vol. 12, pp. 30- 39 ,(1972) , 10.1007/BF00289234