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首页> 外文期刊>International journal of non-linear mechanics >Construction of global Riemann solutions with delta-type initial data for a thin film model with a perfectly soluble anti-surfactant solution
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Construction of global Riemann solutions with delta-type initial data for a thin film model with a perfectly soluble anti-surfactant solution

机译：具有完全可溶性抗表面活性剂溶液的薄膜模型的三醇型初始数据的全局riemann解决方案

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摘要

The global solutions of an extended Riemann problem for a thin film model with a perfectly soluble anti surfactant solution belonging to the Temple class with delta-type initial data are constructed in fully explicit forms for all possible situations. The method used is to perturb the delta-type initial data into initial data consisting of three piecewise constant states, such that the wave interaction problems have been extensively studied, including the interaction between a delta shock wave with a rarefaction (or shock) wave. The global solutions of the extended Riemann problem are obtained by letting the perturbation parameter tend to zero. We find that the initial Dirac delta function propagates along either the line of delta shock wave or the line of contact discontinuity. In addition, we find that some interesting nonlinear phenomena occur during the process of constructing the global solutions, such as a delta shock wave that separates into a shock wave and a delta contact discontinuity.
机译：具有属于Telta-Type初始数据的具有完美可溶性抗表面活性剂溶液的薄膜模型的扩展Riemann问题的全局解决方案是以完全明确的形式构建所有可能的情况。使用的方法是将δ型初始数据扰流到由三个分段恒定状态组成的初始数据，使得已经广泛研究了波相互作用问题，包括具有稀释（或冲击）波的Δ冲击波之间的相互作用。通过让扰动参数趋于为零，获得了扩展riemann问题的全局解决方案。我们发现初始DIRAC DELTA函数沿Δ冲击波或接触不连续线传播。此外，我们发现在构建全局解决方案的过程中发生一些有趣的非线性现象，例如分离成冲击波的三角声冲击波和Δ接触不连续性。

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