Stationary Fix-Caginalp equation with non-local term

DOI10.1016/j.na.2008.12.007zbMath1185.35198OpenAlexW1993404546MaRDI QIDQ1026094

Takashi Suzuki, Souhei Tasaki

Publication date: 24 June 2009

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.2008.12.007

zbMATH Keywords

dual variationFix-Caginalp modelnon-isotermal phase transitionnon-local elliptic problem

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Stability in context of PDEs (35B35) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Bifurcations in context of PDEs (35B32) Viscous-inviscid interaction (76D09)

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Secondary bifurcation for a nonlocal Allen-Cahn equation ⋮ Nonlocal eigenvalue problems arising in a generalized phase-field-type system ⋮ Stability and spectral comparison of a reaction-diffusion system with mass conservation ⋮ Asymptotic behavior of equilibrium states of reaction-diffusion systems with mass conservation ⋮ Representation formulas of solutions and bifurcation sheets to a nonlocal Allen-Cahn equation ⋮ All global bifurcation diagrams of stationary solutions to a phase field model ⋮ Global solution branches for a nonlocal Allen-Cahn equation ⋮ Lyapunov function and spectrum comparison for a reaction-diffusion system with mass conservation ⋮ On a variational problem arising from the three-component FitzHugh-Nagumo type reaction-diffusion systems ⋮ Global dynamics of a reaction-diffusion system with mass conservation ⋮ Spike solutions for a mass conservation reaction-diffusion system

Cites Work

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• Asymptotic behavior of the solution to the non-isothermal phase separation
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• Global behaviour of solution branches for some Neumann problems depending on one or several parameters.
• On the structure of equilibrium phase transitions within the gradient theory of fluids
• Finite dimensional exponential attractor for the phase field model
• Stability of the steady state for the Falk model system of shape memory alloys
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