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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 \align u_t(x,t) & = Au_{xx}(x,t),\quad 0< x< 1,\ t>0,\\ A_1u(0,t)+B_1u_x(0,t) & = 0\in\bbfC^m,\quad t>0,\\ A_2 u(1,t)+B_2u_x(1,t) & = 0\in\bbfC^m,\quad t>0,\endalign where $u(x,t)$ lies in $\bbfC^m$ and $A_1,A_2$, $B_1,B_2$, and $A$ are matrices in $\bbfC^m$. It is an extension of [{\it L. Jódar}, {\it E. Navarro} and {\it J. A. Martin}, Proc. Edinb. Math. Soc., II. Ser. 43, No. 2, 269-293 (2000; Zbl 0949.35033)].

##### MSC:
 35P05 General topics in linear spectral theory of PDE 35M10 PDE of mixed type 35C10 Series solutions of PDE 15A24 Matrix equations and identities
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##### References:
 [1] Martin, J. A.; Navarro, E.; Jódar, L.: Exact and analytic-numerical solutions of strongly coupled mixed diffusion problems. Proc. edinburg math soc. 43, 1-25 (2000) · Zbl 0949.35033 [2] Campbell, S. L.: Singular systems of differential equations. (1980) · Zbl 0419.34007 [3] Axelsson, O.: Iterative solution methods. (1996) · Zbl 0845.65011 [4] Dunford, N.; Schwartz, J.: Linear operators, part I. (1957) · Zbl 0128.34803 [5] Rao, C. R.; Mitra, S. K.: Generalized inverses of matrices and its applications. (1971) · Zbl 0236.15004 [6] Saks, S.; Zygmund, A.: Analytic functions. (1971) · Zbl 0136.37301