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Soler, Vicente; Defez, Emilio; Capilla, Roberto; Verdoy, José Antonio

On the exact series solution for nonhomogeneous strongly coupled mixed parabolic boundary value problems. (English) Zbl 1474.35364

Abstr. Appl. Anal. 2014, Article ID 826860, 10 p. (2014).
Summary: An exact series solution for nonhomogeneous parabolic coupled systems of the type \(u_t - A u_{x x} = G \left(x, t\right), A_1 u \left(0, t\right) + B_1 u_x \left(0, t\right) = 0, A_2 u \left(l, t\right) + B_2 u_x \left(l, t\right) = 0, 0 < x < 1, t > 0, u \left(x, 0\right) = f \left(x\right)\), where \(A_1, A_2, B_1\), and \(B_2\) are arbitrary matrices for which the block matrix \(\begin{pmatrix} A_1 & B_1 \\ A_2 & B_2 \end{pmatrix}\) is nonsingular, and \(A\) is a positive stable matrix, is constructed.

MSC:

35K20 Initial-boundary value problems for second-order parabolic equations
35C10 Series solutions to PDEs
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\textit{V. Soler} et al., Abstr. Appl. Anal. 2014, Article ID 826860, 10 p. (2014; Zbl 1474.35364)
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