Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 156, pp. 119.
Properties of solution diagrams for bistable equations
Pavel Drabek, Radim Hosek
Abstract:
Bistable equation serves as a simple model of phase transition at an
appropriate critical temperature. The structure of its stationary
solutions determines the dynamics of the evolutionary model.
The norm of a stationary solution depending on the diffusion coefficient
is usually depicted in a solution diagram. As far as we know,
the qualitative properties of such diagram like continuity and
differentiability have not been proved rigorously yet.
The purpose of our paper is to fill in this gap.
Submitted April 1, 2015. Published June 11, 2015.
Math Subject Classifications: 34B15, 34B16.
Key Words: Bistable equation; solution diagram; time map.
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Pavel Drabek
Department of Mathematics and NTIS
University of West Bohemia
Univerzitni 22, 306 14 Plzen, Czech Republic
email: pdrabek@kma.zcu.cz


Radim Hosek
Department of Mathematics and NTIS
University of West Bohemia
Univerzitni 22, 306 14 Plzen, Czech Republic
email: radhost@ntis.zcu.cz

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