Buffer phenomenon in the spatially one-dimensional Swift-Hohenberg equation
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We consider a boundary value problem for the spatially one-dimensional Swift-Hohenberg equation with zero Neumann boundary conditions at the endpoints of a finite interval. We establish that as the length l of the interval increases while the supercriticality ɛ is fixed and sufficiently small, the number of coexisting stable equilibrium states in this problem indefinitely increases; i.e., the well-known buffer phenomenon is observed. A similar result is obtained in the 2l-periodic case.
KeywordsEquilibrium State STEKLOV Institute Solvability Condition Dissipative Structure Instability Domain
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