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Steady states solutions of Allen-Cahn equation by computer algebra. (English) Zbl 1338.35007

Summary: We consider the analytical solution and numerical approximation of the celebrated steady states Allen-Cahn equation. We present a computer code to solve and plot the solutions using Maxima software.

MSC:

35-04 Software, source code, etc. for problems pertaining to partial differential equations
34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations
35K58 Semilinear parabolic equations
35K20 Initial-boundary value problems for second-order parabolic equations
82C26 Dynamic and nonequilibrium phase transitions (general) in statistical mechanics

Software:

Maxima
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References:

[2] Atkinson, K.; Han, W., Theoretical numerical analysis: a functional analysis framework, (Texts in Applied Mathematics, vol. 39 (2009), Springer) · Zbl 1181.47078
[3] Brezis, H., Functional Analysis, Sobolev spaces and Partial Differential Equations (2010), Springer · Zbl 1218.46002
[4] Caginalp, G., An analysis of phase field model of a free boundary, Arch. Ration. Mech. Anal., 92, 205-245 (1986) · Zbl 0608.35080
[5] Chen, L. Q., Phase-field models for microstructural evolution, Ann. Rev. Mater. Res., 32, 113-140 (2002)
[8] Moelans, N.; Blanpain, B.; Wollants, P., An introduction to phase-field modeling of microstructure evolution, Comp. Coupl. Phase. Diag. Thermo., 32, 268-294 (2008)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.