Evolutionary boundary delay equations
Abstract
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.
Related
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BibTeX
@misc{aigner2026evolutionary,
title = {{Evolutionary boundary delay equations}},
author = {Bernhard Aigner},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.10307},
eprint = {2607.10307},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.10307},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Evolutionary boundary delay equations
AU - Bernhard Aigner
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2607.10307
UR - https://arxiv.org/abs/2607.10307
AB - 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.
ER -