296 papers
This paper establishes the linearized stability of non-isolated equilibria for quasilinear parabolic problems within interpolation spaces, utilizing a flexible approach with low regularity requirements on the semilinear term to extend previous maximal regularity results and apply to concrete models like the Hele-Shaw problem and fractional mean curvature flow.
This paper investigates the one-dimensional Klein-Gordon equation and demonstrates that in spacelike quarter-planes, solutions exhibiting insufficient growth satisfy a Liouville phenomenon where their values on the two linear edges are uniquely determined by one another, analogous to classical theorems for harmonic functions.
This paper establishes a unified canonical framework linking the Maximal Entropy Simple Symmetric Exclusion Process to both Unitary Dyson Brownian Motion and Free Unitary Brownian Motion by leveraging Schur polynomials and symmetric group characters to derive explicit spectral decompositions and hydrodynamic limits that reveal entropic forces and nonlinear transport equations.
This paper investigates the functional analytic properties of "localized" locally convex topologies to characterize distributions arising as divergences of vector fields, demonstrating that while these topologies are sequential, they generally lack standard properties like being Fréchet-Urysohn or barrelled, and establishing a semireflexivity condition that yields a general existence theorem for solving .
This paper establishes simple sufficient conditions for the rapid stabilization of general linear systems with a Riesz basis of eigenvectors by employing an -equivalence approach via Fredholm transformations, thereby proving that such systems can be transformed into exponentially stable systems with arbitrarily large decay rates and improving existing results for non-parabolic operators.
This paper proposes a novel semi-implicit numerical scheme based on a stochastic scalar auxiliary variable (SSAV) reformulation for the stochastic Cahn--Hilliard equation with multiplicative noise, which incorporates Itô correction terms to achieve optimal strong convergence of order one-half while preserving the energy evolution law.
This paper establishes unweighted Hardy-type inequalities on step-two Carnot groups with one-dimensional vertical layers by employing a quantitative integration-by-parts mechanism that substitutes the non-horizontal Euler vector field with a controlled horizontal one, yielding explicit optimal constant bounds for the Heisenberg group and generalized non-isotropic structures.
This paper investigates the Wasserstein gradient flow of semi-discrete energies relevant to urban planning and uniform quantization by proving the convergence of the JKO scheme to a singularly coupled PDE-ODE system, analyzing its qualitative properties such as atomic convergence to Laguerre cell barycenters, and validating these findings through numerical simulations that reveal dynamic crystallization phenomena.
This paper establishes optimal regularity and provides a complete characterization of higher-order expansions for solutions to linear kinetic Fokker-Planck equations near the grazing set in bounded domains, significantly improving upon previous results that only guaranteed low-order Hölder continuity.
This paper establishes sharp estimates for functions harmonic with respect to -dependent rectilinear stable processes in balls under radial exterior data, utilizing the construction of global barrier functions for the associated -dependent rectilinear fractional Laplacian.
This paper introduces a flux-limited viscosity solution framework for evolutive Hamilton-Jacobi equations with time-measurable Hamiltonians and discontinuous flux limiters on a 1-dimensional junction, proving a comparison principle and establishing existence results for convex cases via optimal control.
This paper establishes the existence of nonlinear wave operators and proves small-data asymptotic completeness for the Maxwell-Higgs system with scalar potential on subextremal Kerr spacetimes by constructing a gauge-invariant scattering map that relies on a transfer principle from linear estimates, provided the absence of superradiant instability.
This paper establishes that geodesic disks are the unique domains maximizing the first non-trivial Neumann eigenvalue among all simply connected regions of the sphere with a fixed area.
This paper utilizes Clifford algebra to derive a hydrodynamics formulation for a modified Dirac equation featuring a nonlinear mass term that preserves homogeneity and admits a chiral split, while also proving the global existence of solutions for a regularized version of the equation.
This paper establishes the convergence of an age-structured mechanical model for tumor growth, which accounts for cell life-cycles and pressure-driven proliferation, to a Hele-Shaw free boundary problem governed by a nonlinear Darcy's law in the incompressible limit.
This paper demonstrates that the trace-free Einstein tensor cannot be derived from any local action functional via variation with respect to the metric, even when the requirement of diffeomorphism invariance is removed.