Local and blowing-up solutions for an integro-differential diffusion equation and system

Meiirkhan Borikhanov and Berikbol T. Torebek

Chaos, Solitons & Fractals, 2021, vol. 148, issue C

Abstract: In the present paper, the semilinear integro-differential diffusion equation and system with singular in time sources are considered. An analog of Duhamel’s principle for the linear integro-differential diffusion equation is proved. Using Duhamel’s principle, a representation of the solution and the well-posedness of the initial problem for the linear integro-differential diffusion equation are established. The results on the existence of local integral solutions and the nonexistence of global solutions to the semilinear integro-differential diffusion equation and system are presented.

Keywords: Blow-up; Global weak solution; Integral solution; Integro-differential diffusion equation (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:148:y:2021:i:c:s0960077921003957

DOI: 10.1016/j.chaos.2021.111041

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