1945 papers
This paper demonstrates that the Modified Method of Characteristics (MMOC) offers a computationally efficient and accurate alternative to Lax-Friedrichs and Lax-Wendroff schemes for the inverse design of the Doswell frontogenesis equation, despite not preserving identity conservation.
These notes primarily focus on the Boundary Control method for solving inverse coefficient determination problems in wave equations, while also providing a brief overview of the geometric optics approach.
This paper establishes the existence, uniqueness, and global asymptotic stability of positive entire solutions for a parabolic-parabolic chemotaxis model with logistic sources in heterogeneous bounded domains by identifying specific parameter regions where the system converges to a unique steady state regardless of initial conditions.
This paper establishes the local null controllability of the energy-critical nonlinear Schrödinger equation in at the level by first proving well-posedness via Strichartz estimates, demonstrating linear controllability through the Hilbert uniqueness method, and finally extending the result to the nonlinear case using a perturbation argument.
This paper characterizes the self-adjoint, unitary, and contractive extensions of Airy and Schrödinger operators on looping-edge graphs by utilizing abstract techniques involving self-orthogonal subspaces and indefinite inner product spaces to describe their boundary conditions at the central vertex.
This paper constructs smooth finite-time blow-up solutions with quantized rates for the Calogero--Moser derivative nonlinear Schrödinger equation by leveraging its integrable Lax pair structure and hierarchy of conservation laws through a forward modulation analysis, offering a simplified alternative to previous repulsivity-based methods.
This paper establishes that within a fixed connectivity class, the spectral support minimizing the average intensity of a focusing Nonlinear Schrödinger equation soliton condensate containing a prescribed anchor set is a compact set composed of critical trajectories of a quadratic differential derived from the associated hyperelliptic Riemann surface.
This paper establishes improved regularity estimates, non-degeneracy properties, and Liouville-type results for viscosity solutions to degenerate or singular fully nonlinear dead-core systems with strong absorption terms and Hénon-type equations, providing new insights even for models involving degenerate Laplacian operators.
This paper establishes the uniqueness of complete non-compact Ricci flows under scaling-invariant curvature bounds by solving the Ricci-harmonic map heat flow in unbounded curvature backgrounds, thereby generalizing previous results and proving a strong uniqueness theorem for three-dimensional flows starting from uniformly non-collapsed, non-negatively curved manifolds.
This paper establishes a rigorous mathematical solution theory for the evolution of an inextensible, closed elastic filament immersed in a 3D Stokes fluid, governed by Euler-Bernoulli beam theory and coupled via the slender body Neumann-to-Dirichlet map, thereby providing a foundational justification for widely used computational models of slender body dynamics.
This paper establishes that shock formation in general first-order strictly hyperbolic systems in one spatial dimension is locally self-similar and universal, mirroring the behavior of the inviscid Burgers' equation, and derives an analytical formula for this universal solution.
This paper provides a corrigendum to the authors' previous work in the *Journal of Differential Equations* by making minor corrections to the assumptions and proof of Theorem 1.2 regarding optimal time-decay estimates for an Oldroyd-B model with zero viscosity.
This paper presents and analyzes a two-scale mathematical model for colloidal deposition in porous media with evolving microstructures, establishing weak solvability for the non-clogging regime and demonstrating through numerical simulations how local clogging impacts effective transport and storage properties.
This paper establishes a rigorous mathematical framework linking laminar-turbulent transition to the local regularity collapse of Leray weak solutions in the Navier-Stokes equations, deriving a transition time scaling of that aligns with classical experimental observations.
This paper investigates one-dimensional nonlocal elliptic transmission problems with sign-changing coefficients by establishing weak T-coercivity, proposing a reconstructed formulation with explicit interface lifting, and proving the convergence of a finite element discretization to the classical local problem as the fractional parameter approaches unity.
This paper establishes a global uniqueness theorem for simultaneously reconstructing obstacle geometry and impedance boundary conditions from multi-frequency near-field backscattering data using high-frequency asymptotic expansions, and proposes a novel three-stage numerical framework that achieves robust and efficient reconstruction without solving the direct scattering problem.
This paper extends the conformal mapping approach to weakly transversal surface waves over topography by deriving a Kadomtsev-Petviashvili type equation in conformal variables that accommodates non-smooth bottom features through the use of effective depth, thereby unifying and extending existing weakly nonlinear dispersive wave models.
This paper establishes sharp mean Hadamard inequalities in two dimensions to prove the uniqueness of minimizers for integral functionals with polyconvex integrands under mixed boundary conditions, supported by computational experiments.
This paper introduces a novel method based on the concept of atoms on discrete sets to derive both exact particular solutions and approximate solutions for higher-order non-homogeneous Cauchy-Euler equations using approximate roots of their characteristic polynomials.
This paper investigates the existence, uniqueness, and qualitative long-time behavior of parabolic-elliptic evolution systems defined on a domain partitioned into two subregions with local and nonlocal operators, demonstrating mass conservation, energy-driven convergence to equilibrium, and the system's emergence as a singular limit of a purely parabolic problem.