发表机构
TU Bergakademie Freiberg（弗莱贝格矿业工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究将演化偏微分方程适定性结果扩展到含非自治材料行为问题类，构建框架处理相关延迟边值问题，能特殊处理多种边界条件，通过应用展示理论可行性与通用性。
AI 中文摘要
最近关于具有状态依赖非齐次性的演化偏微分方程的适定性结果被扩展到包含非自治材料行为的更大问题类。这种推广有助于构建一个能够容纳与演化偏微分方程相关的延迟边值问题的框架。结果允许对具有状态依赖延迟的狄利克雷和诺伊曼类边界条件进行特殊处理。通过使用扩展状态空间，可以处理涉及材料定律中的非自治延迟和强迫项中的状态依赖延迟的复杂边界条件。该方法首次系统地处理了涉及状态依赖延迟的几个经典边界条件的适定性。通过应用于具有狄利克雷、诺伊曼、罗宾、温策尔 - 罗宾和列昂托维奇边界条件的抛物型和双曲型偏微分方程，展示了该理论的可行性和通用性。
英文摘要
Recent well-posedness results for evolutionary partial differential equations with state-dependent inhomogeneity are extended to a larger problem class incorporating nonautonomous material behaviour. This generalization facilitates the formulation of a framework able to accommodate delayed boundary value problems related to evolutionary partial differential equations. The results permit the ad hoc treatment of Dirichlet- and Neumann-like boundary conditions with state-dependent delay. Complex boundary conditions involving nonautonomous delay in the material law and state-dependent delay in the forcing term can be accommodated by use of extended state spaces. This approach provides the first systematic treatment addressing well-posedness of several classical boundary conditions involving state-dependent delay. The viability and versatility of the theory is showcased by applications to parabolic and hyperbolic partial differential equations with Dirichlet, Neumann, Robin, Wentzell-Robin and Leontovich boundary conditions.
