Vol. 7, No. 6, 2014

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Numerical results on existence and stability of steady state solutions for the reaction-diffusion and Klein–Gordon equations

Miles Aron, Peter Bowers, Nicole Byer, Robert Decker, Aslihan Demirkaya and Jun Hwan Ryu

Vol. 7 (2014), No. 6, 723–742

In this paper, we study numerically the existence and stability of the steady state solutions of the reaction-diffusion equation, ut auxx u + u3 = 0, and the Klein–Gordon equation, utt + cut auxx u + u3 = 0, with the boundary conditions: u(1) = u(1) = 0. We show that as a varies, the number of steady state solutions and their stability change.

reaction-diffusion, Klein–Gordon equation, stability, steady state solutions
Mathematical Subject Classification 2010
Primary: 35B30, 35B32, 35B35, 35K57, 35L71
Received: 5 December 2012
Revised: 29 October 2013
Accepted: 5 November 2013
Published: 20 October 2014

Communicated by John Baxley
Miles Aron
University of Zurich
Sonneggstrasse 23
CH-8006 Zurich
Peter Bowers
Harvard University
230 Chestnut Street
Cambridge, MA 02139
United States
Nicole Byer
Brown University
45 Prospect Street
Providence, RI 02912
United States
Robert Decker
University of Hartford
200 Bloomfield Ave
West Hartford, CT 06117
United States
Aslihan Demirkaya
University of Hartford
Dano Hall 210
200 Bloomfield Ave
West Hartford, CT 06117
United States
Jun Hwan Ryu
Yale University
206 Elm Street #205495
New Haven, CT 06520-5495
United States