Multi-layer Local Minimum Solutions of the Bistable Equation in Noncylindrical Domains
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چکیده
منابع مشابه
Multi-layer Local Minimum Solutions of the Bistable Equation in Noncylindrical Domains
We construct local minimum solutions for the semilinear bistable equation by minimizing the corresponding functional near some approximate solutions, under the hypothesis that certain global minimum solutions are isolated. The key is a certain characterization of Palais-Smale sequences and a proof that the functional takes higher values away from the approximate solutions.
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15 صفحه اولMultiple Layered Solutions of the Nonlocal Bistable Equation
The nonlocal bistable equation is a model proposed recently to study materials whose constitutive relations among the variables that describe their states are nonlocal. It resembles the local bistable equation (the Allen-Cahn equation) in some way, but contains a much richer set of solutions. In this paper we consider two types of solutions. The first are the periodic solutions on a finite inte...
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We discuss instability and existence issues for the nonlocal bistable equation. This model arises as the Euler-Lagrange equation of a nonlocal, van der Waals type functional. Taking the viewpoint of the calculus of variations, we prove that for a class of nonlocalities this functional does not admit nonconstant C local minimizers. By taking variations along nonsmooth paths, we give examples of ...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1997
ISSN: 0022-0396
DOI: 10.1006/jdeq.1997.3284