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Exact and analytic-numerical solutions of strongly coupled mixed diffusion problems. (English) Zbl 0949.35033

Coupled partial differential systems with coupled boundary conditions are frequent in quantum mechanical scattering problems, chemical physics, thermoelastoplastic modelling, coupled diffusion problems and other fields. In this paper systems of the type

u t (x,t)-Au xx (x,t)=0,0<x<1,t>0,A 1 u(0,t)+B 1 u x (0,t)=0,t>0,A 2 u(1,t)+B 2 u x (1,t)=0,t>0,u(x,0)=f(x),0x1,

are considered, where the unknown u=(u 1 ,u 2 ,,u m ) T and f=(f 1 ,f 2 ,,f m ) T are m-dimensional vectors, A i ,B i ,i=1,2 are m×m complex matrices, where no simultaneous diagonalizable hypothesis is assumed, and A is a positive stable matrix, such that Re(z)>0 for all eigenvalues z of A. The construction of exact and analytical-numerical solutions with apriori bounds is shown. Given an admissible error ε and a bounded subdomain D, an approximate solution whose error with respect to an exact series solution is less than ε uniformly in D is constructed.

35C10Series solutions of PDE
15A24Matrix equations and identities
35M10PDE of mixed type