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2015 A dynamical system for a nonlocal parabolic equation with exponential nonlinearity
Tosiya Miyasita
Rocky Mountain J. Math. 45(6): 1897-1917 (2015). DOI: 10.1216/RMJ-2015-45-6-1897

Abstract

We consider a nonlocal parabolic and the corresponding elliptic equation with exponential nonlinearity. At first, we study the set of a stationary solution and compute its Morse index. Next, we obtain the time-global solution in the use of the Lyapunov function and define the dynamical system. Finally, we construct an exponential attractor by a squeezing property.

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Tosiya Miyasita. "A dynamical system for a nonlocal parabolic equation with exponential nonlinearity." Rocky Mountain J. Math. 45 (6) 1897 - 1917, 2015. https://doi.org/10.1216/RMJ-2015-45-6-1897

Information

Published: 2015
First available in Project Euclid: 14 March 2016

zbMATH: 1338.35234
MathSciNet: MR3473161
Digital Object Identifier: 10.1216/RMJ-2015-45-6-1897

Subjects:
Primary: 35K55
Secondary: 35J60, 37L25

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

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Vol.45 • No. 6 • 2015
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