Abstract
We employ the Galerkin method to prove the global existence of weak solutions to a phase-field model which is suitable to describe a sort of interface motion driven by configurational forces. The higher-order derivative of unknown S exists in the sense of local weak derivatives since it may be not summable over the original open domain. The existence proof is valid in the one-dimensional case.
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The authors would like to sincerely appreciate Prof. Peicheng ZHU for his careful instruction.
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Citation: ZHU, Z. X., GUO, B. L., and FANG, S. M. Global weak solutions to a phase-field model for motion of grain boundaries. Applied Mathematics and Mechanics (English Edition), 43(11), 1777–1792 (2022) https://doi.org/10.1007/s10483-022-2915-9
Project supported by the Science and Technology Commission of Shanghai Municipality of China (No. 20JC1413600)
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Zhu, Z., Guo, B. & Fang, S. Global weak solutions to a phase-field model for motion of grain boundaries. Appl. Math. Mech.-Engl. Ed. 43, 1777–1792 (2022). https://doi.org/10.1007/s10483-022-2915-9
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DOI: https://doi.org/10.1007/s10483-022-2915-9