Rocky Mountain Journal of Mathematics

A dynamical system for a nonlocal parabolic equation with exponential nonlinearity

Tosiya Miyasita

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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.

Article information

Source
Rocky Mountain J. Math., Volume 45, Number 6 (2015), 1897-1917.

Dates
First available in Project Euclid: 14 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1457960341

Digital Object Identifier
doi:10.1216/RMJ-2015-45-6-1897

Mathematical Reviews number (MathSciNet)
MR3473161

Zentralblatt MATH identifier
1338.35234

Subjects
Primary: 35K55: Nonlinear parabolic equations
Secondary: 35J60: Nonlinear elliptic equations 37L25: Inertial manifolds and other invariant attracting sets

Keywords
Nonlocal Morse index Lyapunov function exponential attractor squeezing property

Citation

Miyasita, Tosiya. A dynamical system for a nonlocal parabolic equation with exponential nonlinearity. Rocky Mountain J. Math. 45 (2015), no. 6, 1897--1917. doi:10.1216/RMJ-2015-45-6-1897. https://projecteuclid.org/euclid.rmjm/1457960341


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