Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 1114.35005
Nakashima, Kimie; Tanaka, Kazunaga
Clustering layers and boundary layers in spatially inhomogeneous phase transition problems. (Couches limites dans des problèmes de transition de phase spatialement inhomogènes.) (English)
[J] Ann. Inst. Henri Poincaré, Anal. Non Linéaire 20, No. 1, 107-143 (2003). ISSN 0294-1449

Summary: The authors study the existence of solutions with multiple clustered transition layers for the following inhomogeneous problem of Allen-Cahn type: $$-\varepsilon^2u_{xx}+W_u(x,u)=0 \text{ in } (0,1),\quad u_x(0)=u_x(1)=0,\tag1$$ where $\varepsilon>0$ is a small parameter and $W(x,u)$ is a double-well potential. A typical example of $W(x,u)$ is ${1\over4}h(x)^2(u^2-1)^2$. In particular, they show the existence of solutions with clustered layers and layers.

MSC 2000:: *35B25 Singular perturbations (PDE)
35Q35 Other equations arising in fluid mechanics
34B15 Nonlinear boundary value problems of ODE
34E15 Asymptotic singular perturbations, general theory (ODE)
47J30 Variational methods
76T99 None of the above, but in this section

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]