Exact Eigenvalues and Eigenfunctions Associated with Linearization for Chafee-Infante Problem

MR2271237 Tohru WAKASA Tohru WAKASA Exact Eigenvalues and Eigenfunctions Associated with Linearization for Chafee-Infante Problem Funkcialaj Ekvacioj. Serio Internacia 49 2006 321--336 http://fe.math.kobe-u.ac.jp/FE/FullPapers/49-2/49_321.pdf http://www.ams.org/mathscinet-getitem?mr=MR2271237 In this paper we consider nontrivial stationary solutions to Chafee-Infante problem and the corresponding linearized eigenvalue problem. We introduce a reduced equation to give explicit and simple-looking expressions of some eigenvalues and eigenfunctions to linearized problem. Chafee-Infante problem, Linearized eigenvalue problem, Linearized stability, Eigenvalue, Eigenfunction. 34A05, 34B05, 34B15, 35K57. 49-321 2006 Exact Eigenvalues and Eigenfunctions Associated with Linearization for Chafee-Infante Problem WAKASA, Tohru Tohru WAKASA

1 Chafee, N.; Infante, E. F. A bifurcation problem for a nonlinear partial differential equation of parabolic type Applicable Anal. 4 1974/1975 17-37 MR0440205

2 Smoller, J.; Wasserman, A. Global bifurcation of steady-state solutions J. Differential Equations 39 1981 269-290 MR0607786

3 Brunovský, P.; Fiedler, B. Connecting orbits in scalar reaction diffusion equations II, The complete solution J. Differential Equations 81 1989 106-135 MR1012202

4 Henry, D. Geometric Theory of Semilinear Parabolic Equations Lecture Notes in Mathematics, 840, Springer-Verlag, Berlin/New York 1981 MR0610244 5 Wakasa, T.; Yotsutani, S., in preparation