Generalized solutions of mixed problems for first-order partial functional differential equations |
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Authors: | W Czernous |
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Institution: | (1) Gdansk University of Technology, Gdansk, Poland |
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Abstract: | A theorem on the existence of solutions and their continuous dependence upon initial boundary conditions is proved. The method
of bicharacteristics is used to transform the mixed problem into a system of integral functional equations of the Volterra
type. The existence of solutions of this system is proved by the method of successive approximations using theorems on integral
inequalities. Classical solutions of integral functional equations lead to generalized solutions of the original problem.
Differential equations with deviated variables and differential integral problems can be obtained from the general model by
specializing given operators.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 6, pp. 804–828, June, 2006. |
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Keywords: | |
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