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The asymptotic behavior for a binary alloy in energy and material science:the unified method and its applications

Journal of Ocean Engineering and Science 2024年第4期9卷 373-378页

作者： M.Adel K.Aldwoah F.Alahmadi M.S.Osman Department of Mathematics Faculty of ScienceIslamic University of MadinahMedinaSaudi Arabia Department of Mathematics Faculty of ScienceCairo UniversityGiza 12613Egypt

The Cahn-Hilliard system was proposed to the first time by Chan and Hilliard in *** model(or system of equations)has intrinsic participation energy and materials sciences and depicts significant characteristics of two phase systems relating to the procedures of phase separation when the temperature is *** instance,it can be noticed when a binary alloy(“Aluminum+Zinc”or“Iron+Chromium”)is cooled down *** this case,partially or totally nucleation(nucleation means the appearance of nuclides in the material)is observed:the homogeneous material in the initial state gradually turns into inhomogeneous,giving rise to a very accurate dispersive ***,when the time scale is slower the microstructure becomes *** this work,to the first time,the unified method is presented to investigate some physical interpretations for the solutions of the Cahn-Hilliard system when its coefficients varying with time,and to show how phase separation of one or two components and their concentrations occurs dynamically in the ***,2D and 3D plots are introduced to add more comprehensive study which help to understand the physical phenomena of this *** technique applied in this analysis is powerful and efficient,as evidenced by the computational work and *** technique can also solve a large number of higher-order evolution equations.

关键词： Cahn-Hilliard system Traveling wave solutions the unified method Variable coefficients

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