Finite-time well-posedness, uniqueness, and kernel-stability bounds are proved for diffusion equations with arbitrary finite measure-valued memory, unifying continuous and discrete delay regimes.
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Semigroups of linear operators and applications to partial differential equa- tions, volume 44 of Applied Mathematical Sciences
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Defines resilience evaluation D^ρ π as the L1-limit of scaled dynamic risk measure applied to process increments, and derives its dual representation as worst-case conditional expectation of an effective drift when ρ arises from BSDEs with Lipschitz or quadratic drivers.
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Establishes well-posedness in history space, Lipschitz and weak-star robustness, and compact global attractors with upper semicontinuity for semilinear reaction-diffusion equations with measure-valued delays.
Data-driven spectral submanifold reduction produces low-dimensional delay-free ODE models for nonlinear delayed dynamical systems from measurements alone.
Constructive existence results and explicit solutions for the heat equation with Stieltjes derivatives, covering initial-boundary value problems and multivariable derivator extensions.
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Stability of semigroup smoothing under relatively bounded perturbations yields spectral and eventually positive perturbation theorems for elliptic PDEs.
Plebanski's chiral 2-form formulation of GR reveals additional structure in Einstein's equations and supplies new analytical and numerical tools.
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Well-posedness and kernel stability for diffusion equations with mixed measure-valued memory
Finite-time well-posedness, uniqueness, and kernel-stability bounds are proved for diffusion equations with arbitrary finite measure-valued memory, unifying continuous and discrete delay regimes.