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Application of Rothe’s method to evolution integrodifferential equations. (English) Zbl 0638.65098
Rothe’s method (the method of lines) is applied to evolution integrodifferential equations and to the corresponding variational inequalities of parabolic and hyperbolic type. The construction of the approximate solution is reduced to the solution of the corresponding linear elliptic equations resp. elliptic variational inequalities. The existence of strong solutions and the convergence of the method used are proved. Higher order regularity in t is proved assuming the corresponding compatibility conditions. In the parabolic case the smoothing effect is investigated. Regularity in x-variables is obtained from the corresponding elliptic equations using the structure of approximation scheme. Some numerical aspects of the method used are presented using full (time and space) discretization.
Reviewer: J.Kačur

MSC:
65R20 Numerical methods for integral equations
65K10 Numerical optimization and variational techniques
45K05 Integro-partial differential equations
49J40 Variational inequalities
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