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Pure Mathematics 2020
一类相变模型的弱解存在性的研究
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Abstract:
本文在忽略弹性效应的情况下，研究了一类Neumann边界条件下的序参数不守恒的相场模型。通过引入一个参数κ构造一个修正模型，然后借助巴拿赫不动点定理、Aubin-Lions引理和一系列先验估计，最终得到该模型弱解的整体存在性。
We shall investigate a phase-field model with a non-conserved order parameter which is under Neumann boundary conditions and omitting the effect of elasticity. By introducing a parameter κ to construct a modified model, and then using Banach’s fixed point Theorem, Aubin-Lions lemma and a series of a-priori estimates, the existence of global weak solutions to the model is finally obtained.
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