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Application of Rothe’s method to evolution integrodifferential systems. (English) Zbl 0674.65110
The author considers a system of two quasilinear integrodifferential equations (hyperbolic and parabolic). Rothe’s method (method of lines) is used to prove the existence of a weak solution of the studied system. Uniqueness of a weak solution and its continuous dependence on the right- hand side and on the initial functions are proved too. Moreover, a semidiscrete approximation solution is defined and the rate of convergence of Rothe’s functions in the spaces C and \(L_ 2\) is established.
Reviewer: L.Haçia

MSC:
65R20 Numerical methods for integral equations
45K05 Integro-partial differential equations
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