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On the existence and uniqueness of solution of the Cauchy problem for linear integro-differential equations with operator coefficients
Applications of Mathematics, Tome 16 (1971) no. 1, pp. 64-80
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In the theory of neutron fields some problems arise, which may be described by means of integro-differential equations with initial conditions. The aim of the paper is to state a class of problems covering this physical example and to prove the existence, uniqueness and continuous dependence of their solutions on the given data. A variational approach, presented in a previous author's article, is used to establish the definition of generalized (weak) solutions of the Cauchy problem, which is an extension of the concept of generalized solutions of differential equations.
In the theory of neutron fields some problems arise, which may be described by means of integro-differential equations with initial conditions. The aim of the paper is to state a class of problems covering this physical example and to prove the existence, uniqueness and continuous dependence of their solutions on the given data. A variational approach, presented in a previous author's article, is used to establish the definition of generalized (weak) solutions of the Cauchy problem, which is an extension of the concept of generalized solutions of differential equations.
DOI : 10.21136/AM.1971.103326
Classification : 45J05, 47G05 
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Hlaváček, Ivan. On the existence and uniqueness of solution of the Cauchy problem for linear integro-differential equations with operator coefficients. Applications of Mathematics, Tome 16 (1971) no. 1, pp. 64-80. doi: 10.21136/AM.1971.103326

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[3] Ладыженская О. А.: Смешанная загача для гиперболических уравнений. Москва 1953. | Zbl

[4] Люстерник Л. А., Соболев В. И.: Элементы функционального анализа. Москва 1951. | Zbl

[5] Achieser N. I., Glasmann I. M.: Theorie der linearen Operatoren im Hilbert-Raum. Akademie-Verlag Berlin 1958. | Zbl

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