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.
Pazy.Semigroups of Linear Operators and Applications to Partial Differential Equations
9 Pith papers cite this work. Polarity classification is still indexing.
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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.
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.
The work establishes continuous Fréchet differentiability of the switching-point-to-control map for abstract semilinear parabolic equations and characterizes the convex hull of feasible switching functions via an extended formulation.
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.
citing papers explorer
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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.
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Data-Driven Reduced Modeling of Delayed Dynamical Systems via Spectral Submanifolds
Data-driven spectral submanifold reduction produces low-dimensional delay-free ODE models for nonlinear delayed dynamical systems from measurements alone.
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Constructive solutions of the heat equation with Stieltjes derivatives
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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Nonautonomous systems of evolution inclusions
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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Switching Point Optimization for Abstract Parabolic Equations
The work establishes continuous Fréchet differentiability of the switching-point-to-control map for abstract semilinear parabolic equations and characterizes the convex hull of feasible switching functions via an extended formulation.
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Smoothing of operator semigroups under relatively bounded perturbations
Stability of semigroup smoothing under relatively bounded perturbations yields spectral and eventually positive perturbation theorems for elliptic PDEs.
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General Relativity via differential forms -- explorations in Plebanski's Formalism for GR
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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