Analysis of an iterative scheme of fractional steps type associated to the nonlinear phase-field equation with non-homogeneous dynamic boundary conditions

DOI10.3934/dcdss.2016011zbMath1353.65094OpenAlexW2325150004MaRDI QIDQ321660

Costică Moroşanu, Alain Miranville

Publication date: 14 October 2016

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdss.2016011

zbMATH Keywords

algorithmstabilityconvergencenonlinear parabolic equationboundary value problemsthermodynamicsheat transfererror estimateAllen-Cahn equationnonhomogeneous dynamic boundary conditionsnonlinear phase-field equationtwo-phase systems

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) PDEs in connection with fluid mechanics (35Q35) Stefan problems, phase changes, etc. (80A22) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

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Cites Work

• Asymptotic behavior of the Caginalp phase-field system with coupled dynamic boundary conditions
• A product formula approach to a nonhomogeneous boundary optimal control problem governed by nonlinear phase-field transition system. I: A phase-field model
• Robust exponential attractors for singularly perturbed phase-field equations with dynamic boundary conditions
• Phase-field systems with nonlinear coupling and dynamic boundary conditions
• Thermodynamically consistent models of phase-field type for the kinetics of phase transitions
• The non-isothermal Allen-Cahn equation with dynamic boundary conditions
• On the asymptotic behavior of the Caginalp system with dynamic boundary conditions
• Analysis of a two-phase field model for the solidification of an alloy
• A generalized phase-field system
• Global solution to the Allen-Cahn equation with singular potentials and dynamic boundary conditions
• Long time behavior of the Caginalp system with singular potentials and dynamic boundary conditions
• On the existence, uniqueness and regularity of solutions to the phase-field transition system with non-homogeneous Cauchy-Neumann and nonlinear dynamic boundary conditions
• Existence of global solutions to the Caginalp phase-field system with dynamic boundary conditions and singular potentials
• ATTRACTORS FOR A CAGINALP MODEL WITH A LOGARITHMIC POTENTIAL AND COUPLED DYNAMIC BOUNDARY CONDITIONS
• Optimal control of a phase field model for solidification
• Fractional Steps Scheme to Approximate the Phase-Field Transition System with Non-Homogeneous Cauchy–Neumann Boundary Conditions
• Convergence of the phase field model to its sharp interface limits
• Evolution systems of nonlinear variational inequalities arising from phase change problems
• Numerical approximation for the phase-field transition system
• Approximation of the phase-field transition system via fractional steps method
• Exponential attractors for the Cahn-Hilliard equation with dynamic boundary conditions
• Some questions in the optimal control of distributed systems
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