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Constructing eigenfunctions of strongly coupled parabolic boundary value systems. (English) Zbl 1014.35065

Summary: This paper deals with the study of existence conditions as well as the construction of eigenfunctions of strongly coupled parabolic boundary value partial differential systems

u t (x,t)=Au xx (x,t),0<x<1,t>0,A 1 u(0,t)+B 1 u x (0,t)=0 m ,t>0,A 2 u(1,t)+B 2 u x (1,t)=0 m ,t>0,

where u(x,t) lies in m and A 1 ,A 2 , B 1 ,B 2 , and A are matrices in m . It is an extension of [L. Jódar, E. Navarro and J. A. Martin, Proc. Edinb. Math. Soc., II. Ser. 43, No. 2, 269-293 (2000; Zbl 0949.35033)].

MSC:
35P05General topics in linear spectral theory of PDE
35M10PDE of mixed type
35C10Series solutions of PDE
15A24Matrix equations and identities