Nonlinear evolution equations: model hierarchies and complex fluids (A08)

非线性发展方程是科学和工程中随时间变化的过程的数学模型。我们专注于通过例如时间或空间的非局部性以及例如非单调增长的非标准假设而丰富的模型。我们通过适当的逼近格式的收敛来研究广义解的存在性。在软物质和复杂流体的动力学方面出现了应用。我们的目标是研究近晶相的模型以及液晶的非局域模型，并应用相对能量的新概念。

Nonlinear evolution equations are the mathematical models for time-dependent processes in science and engineering. We focus on models enriched by, e.g., nonlocality in time or space as well as on non-standard assumptions as, e.g., non-monotone growth. We study existence of generalized solutions via convergence of suitable approximation schemes. Applications arise in soft matter and dynamics of complex fluids. We aim to study models for smectic phases as well as nonlocal models of liquid crystals and to apply the new concept of relative energy.