Global existence and uniqueness of solutions for a viscoelastic two-phase model with nonlocal capillarity
Global existence and uniqueness of solutions for a viscoelastic two-phase model with nonlocal capillarity
复制标题
具有非局部毛细管现象的粘弹性两相模型解的全局存在性和唯一性
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
C. Rohde
中科院分区：
文献类型：
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作者：
A. Dressel;C. Rohde
本文的目的是研究一维毛细管粘弹性两相材料初边值问题解的存在性和唯一性。其中，毛细管现象通过非局部相互作用势进行建模。证明依赖于一系列差异近似的统一能量估计：利用这些估计，我们证明了全局弱解的存在。然后，通过[2]中参数的非平凡变体，证明了唯一性和最优正则性。本文的结果也适用于具有非零负部分的相互作用势，并构成时间渐近行为分析的基础。
The aim of this paper is to study the existence and uniqueness of solutions of an initial-boundary value problem for a viscoelastic two-phase material with capillarity in one space dimension. Therein, the capillarity is modelled via a nonlocal interaction potential. The proof relies on uniform energy estimates for a family of difference approximations: with these estimates at hand we show the existence of a global weak solution. Then, by means of a nontrivial variant of the arguments in [2], uniqueness and optimal regularity are proven. The results of this paper also apply to interaction potentials with non-vanishing negative part and constitute a base for an analysis of the time-asymptotic behaviour.