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Zbl 1068.45014
Liang, Jin; Xiao, Ti-Jun
Semilinear integrodifferential equations with nonlocal initial conditions. (English)
[J] Comput. Math. Appl. 47, No. 6-7, 863-875 (2004). ISSN 0898-1221

The paper is concerned with developing existence and uniqueness theorems for the Cauchy problem for semilinear integro-differential equations of convolution type. The sequence of theorems presented extends the existing results and can be applied, as is shown in the final section of the paper, to problems that arise in heat conduction in materials with memory.
[Neville Ford (Chester)]

MSC 2000:: *45J05 Integro-ordinary differential equations
45G10 Nonsingular nonlinear integral equations

Keywords: non-local initial conditions; Cauchy problem; Mild solution; Classical solution; heat conduction in materials with memory; semilinear integro-differential equations of convolution type;

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