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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 \[ \begin{aligned} u_t(x,t) & = Au_{xx}(x,t),\quad 0< x< 1,\;t>0,\\ A_1u(0,t)+B_1u_x(0,t) & = 0\in\mathbb{C}^m,\quad t>0,\\ A_2 u(1,t)+B_2u_x(1,t) & = 0\in\mathbb{C}^m,\quad t>0,\end{aligned} \] where \(u(x,t)\) lies in \(\mathbb{C}^m\) and \(A_1,A_2\), \(B_1,B_2\), and \(A\) are matrices in \(\mathbb{C}^m\). 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:

35P05 General topics in linear spectral theory for PDEs
35M10 PDEs of mixed type
35C10 Series solutions to PDEs
15A24 Matrix equations and identities

Citations:

Zbl 0949.35033
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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), Pitman · Zbl 0419.34007
[3] Axelsson, O., Iterative Solution Methods (1996), Cambridge Univ. Press: Cambridge Univ. Press Cambridge
[4] Dunford, N.; Schwartz, J., Linear Operators, Part I (1957), Interscience: Interscience New York
[5] Rao, C. R.; Mitra, S. K., Generalized Inverses of Matrices and its Applications (1971), John Wiley: John Wiley New York
[6] Saks, S.; Zygmund, A., Analytic Functions (1971), Elsevier: Elsevier Amsterdam · JFM 60.0243.01
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