Local well-posedness is proved for evolutionary PDEs with nonautonomous material laws and state-dependent delay in both forcing and classical boundary conditions via extended state spaces and lifting.
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Existence of L2 solutions holds for a nonlinear electrostatic Maxwell problem with nonlocal dielectricity under a size condition on F, for weak Lipschitz domains, without monotonicity or derivative assumptions on the nonlinearity.
H-convergence of multiplication operators implies nonlocal H-convergence for arbitrary dimensions and more general differential operators without extra structural assumptions.
Extends semigroup methods and measurable selection results to prove global existence for partially nonautonomous evolution inclusion systems under Hausdorff continuity and convexity conditions on couplings.
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Evolutionary boundary delay equations
Local well-posedness is proved for evolutionary PDEs with nonautonomous material laws and state-dependent delay in both forcing and classical boundary conditions via extended state spaces and lifting.
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Nonlinear Media via Nonlocal Homogenisation
Existence of L2 solutions holds for a nonlinear electrostatic Maxwell problem with nonlocal dielectricity under a size condition on F, for weak Lipschitz domains, without monotonicity or derivative assumptions on the nonlinearity.