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Blow-up and stability of a nonlocal diffusion-convection problem arising in Ohmic heating of foods
National Technical University of Athens, GRC.ORCID iD: 0000-0002-9743-8636
National Technical University of Athens, GRC.
2002 (English)In: Differential and Integral Equations, no 3, p. 271-288Article in journal (Refereed) Published
Abstract [en]

We study the blow-up and stability of solutions of the equation ut+ux=uxx+λf(u)/(∫10f(u)dx)2 with certain initial and boundary conditions. When f is a decreasing function, we show that if ∫∞0f(s)ds<∞, then there exists a λ∗>0 such that for λ>λ∗, or for any 0<λ≤λ∗ but with initial data sufficiently large, the solutions blow up in finite time. If ∫∞0f(s)ds=∞, then the solutions are global in time. The stability of solutions in both cases is discussed. We also study the case of f being increasing.

Place, publisher, year, edition, pages
Khayyam , 2002. no 3, p. 271-288
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-88630OAI: oai:DiVA.org:kau-88630DiVA, id: diva2:1638763
Available from: 2022-02-17 Created: 2022-02-17 Last updated: 2022-11-21Bibliographically approved

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https://projecteuclid.org/journals/differential-and-integral-equations/volume-15/issue-3/Blow-up-and-stability-of-a-nonlocal-diffusion-convection-problem/die/1356060861.full

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Kavallaris, Nikos I.

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