Global solvability for the heat equation with boundary flux governed by nonlinear memory

Anderson, Jeffrey; Deng, Keng; Dong, Zhihua

doi:10.1090/S0033-569X-2011-01238-X

Authors: Jeffrey R. Anderson, Keng Deng and Zhihua Dong
Journal: Quart. Appl. Math. 69 (2011), 759-770
MSC (2010): Primary 35B44, 35K05, 35K20
DOI: https://doi.org/10.1090/S0033-569X-2011-01238-X
Published electronically: July 1, 2011
MathSciNet review: 2893999
Full-text PDF Free Access

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Abstract: We introduce the study of global existence and blowup in finite time for the heat equation with flux at the boundary governed by a nonlinear memory term. Via a simple transformation, the model may be written in a form which has been introduced in previous studies of tumor-induced angiogenesis. The present study is also in the spirit of extending work on models of the heat equation with local, nonlocal, and delay nonlinearities present in the boundary flux. Additionally, we provide a brief summary of related studies regarding heat equation models where memory terms are incorporated within reaction or diffusion.

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