250 papers
This paper presents a minimal port-Hamiltonian formulation for interacting particle systems to analyze their stability and mean-field limits, while simultaneously issuing an erratum that corrects a previous claim regarding trajectory compactness by providing a counterexample for repulsive interactions and a revised proof for Hamiltonian gradient convergence.
This paper establishes that the space of continuous distribution-valued solutions to a linear partial differential equation with polynomial coefficients possesses the concatenation property if and only if the equation is first-order in the time derivative.
This paper establishes a detailed equivalence between semilinear elliptic PDEs with isolated singularities and stationary nonlinear Schrödinger equations with point interactions in dimensions two and three, enabling the application of variational methods to prove the existence of infinitely many singular and nodal solutions.
This paper establishes the convergence of Lie-Trotter and Strang splitting schemes for the Gross-Pitaevskii equation with time-dependent potentials and non-zero boundary conditions in Zhidkov spaces, while demonstrating the conservation of generalized mass, near-preservation of energy, and investigating quantum vortex nucleation in relevant experimental settings.
This paper improves the known threshold for the flexibility of isometric immersions of -dimensional Riemannian metrics into by proving that any short immersion can be approximated by such immersions for when , utilizing a refined convex integration scheme with enhanced iterative integration by parts.
This paper establishes the local well-posedness of the quartic Zakharov-Kuznetsov equation on for all Sobolev regularities by leveraging recent bilinear smoothing and linear Strichartz-type estimates.
This paper establishes a Barta-type formulation for the -Laplacian on Riemannian manifolds to derive sharp lower bounds for the -fundamental tone without boundary regularity assumptions, leading to nonlinear extensions of classical spectral comparison theorems and geometric characterizations for minimal immersions.
This paper establishes the uniqueness of coefficients in a doubly nonlinear parabolic equation by reducing the problem to an elliptic inverse problem, where the conductivity is recovered via asymptotic expansions of the Dirichlet-to-Neumann map and the remaining potential is determined through linearization.
This paper characterizes an agent's optimal consumption, investment, and time-varying job-switching strategies over a finite horizon by reducing the dual problem to a parabolic double obstacle problem with time-dependent obstacles, for which existence, uniqueness, and free boundary smoothness are rigorously established using PDE theory.
This paper develops extensions of parametric nonlinear Schrödinger equations for phase-sensitive optical resonance that preserve the curve lengthening bifurcation by constructing specific down-phase self-interaction operators, thereby maintaining linear stability while enabling a sign flip in the normal velocity's linear term.
This paper provides an affirmative solution to an open problem posed by Brezis and Mironescu in their book *Sobolev Maps to the Circle*, demonstrating that the least mass of area-minimizing integral rectifiable currents with a smooth boundary equals the infimum of areas among smoothly immersed submanifolds sharing that boundary.
This paper establishes the global existence, uniform-in-time boundedness, and exponential convergence to steady states for classical solutions of two-dimensional Keller-Segel-Navier-Stokes systems with signal-dependent power-law decaying sensitivities by employing localized energy estimates and a novel interpolation inequality.
This paper establishes the existence of solutions for a class of integro-differential equations involving the difference between Laplacian and bi-Laplacian operators in unbounded domains by applying fixed point techniques and solvability conditions for non-Fredholm elliptic operators.
This paper rigorously establishes the low Mach number limit and derives explicit convergence rates for a three-dimensional viscous compressible two-fluid model with algebraic pressure closure, proving that its well-prepared strong solutions converge to the incompressible Navier–Stokes equations as the Mach number tends to zero.
This paper constructs the parametrix for elliptic Gevrey pseudodifferential operators by establishing a Banach algebra structure for formal Gevrey symbols, which is then applied to derive estimates for adiabatic projectors in the Gevrey setting.
This paper demonstrates that entropy acts as a driving force in various evolution equations because it characterizes the invariant measure of an underlying stochastic process, thereby unifying diverse examples from stochastic processes, gradient flows, and GENERIC systems under a single principle.
This paper establishes the existence of sign-changing solutions to a critical elliptic equation involving a Yamabe type operator on a compact manifold with boundary, contingent upon specific geometric conditions.
This paper establishes the existence, uniqueness, and sharp boundary asymptotics of large solutions to semilinear elliptic equations with gradient-dependent terms and singular weights, while also proving their strict convexity and identifying them as value functions for infinite-horizon stochastic optimal control problems.
This paper investigates an inverse Robin spectral problem for the nonlinear -Laplace operator by establishing a thin-coating asymptotic limit, proving the uniqueness of the Robin coefficient via linearization and unique continuation, and deriving a conditional local Hölder-type stability estimate.
This paper establishes higher pointwise regularity for nonnegative classical solutions of fully fractional parabolic equations by providing a unified proof based on novel equivalent definitions of pointwise function spaces and the integral representation of the fractional heat kernel.