Global existence and divergence of critical solutions of a non-local parabolic problem in Ohmic heating process

DOI10.1016/J.NA.2004.04.012zbMath1059.35063OpenAlexW2028306574MaRDI QIDQ1883097

Dimitrios E. Tzanetis, Andrew A. Lacey, Nikos I. Kavallaris

Publication date: 1 October 2004

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2004.04.012

zbMATH Keywords

Comparison methodsglobal-unbounded solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60)

Related Items (7)

A multi-species chemotaxis system: Lyapunov functionals, duality, critical mass ⋮ On a nonlocal problem modelling Ohmic heating in planar domains ⋮ Diffusion-Driven Blow-Up for a Nonlocal Fisher-KPP Type Model ⋮ Blow-up for a nonlocal parabolic equation ⋮ Further spectral properties of uniformly elliptic operators that include a non-local term ⋮ Grow-up of critical solutions for a non-local porous medium problem with Ohmic heating source ⋮ Asymptotic behaviour for a non-local parabolic problem

Cites Work

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• Temperature Surges in Current-Limiting Circuit Devices
• On a nonlocal elliptic equation with decreasing nonlinearity arising in plasma physics and heat conduction
• Thermal runaway in a non-local problem modelling Ohmic heating. Part II: General proof of blow-up and asymptotics of runaway
• Thermal runaway in a non-local problem modelling Ohmic heating: Part I: Model derivation and some special cases

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