293 papers
This paper defines a fractional Ito stochastic integral with respect to a randomly scaled fractional Brownian motion using an -transform approach, establishes the corresponding Ito formula, and applies it to investigate generalized time-fractional evolution equations.
This paper establishes the Fujita-type critical exponents for semilinear heat equations driven by mixed local-nonlocal operators, demonstrating that the critical threshold is governed solely by the nonlocal component and thereby refining existing results for both forced and unforced cases.
This paper establishes a complete characterization of the compactness of Sobolev embeddings for radially symmetric functions on and weighted balls within the general framework of rearrangement-invariant function spaces by developing novel techniques that overcome the limitations of previous methods restricted to domains of finite measure.
This paper investigates the blowup phenomena of Toda systems, which generalize the Liouville equation via simple Lie algebras, by providing concrete examples of blowup masses that correspond to Weyl groups.
This paper establishes the well-posedness, instantaneous separation, and long-time convergence to stationary states for a two-dimensional bulk-surface Cahn--Hilliard model with non-degenerate mobility and singular potentials, utilizing a novel regularity theory for bulk-surface elliptic systems to prove uniqueness and continuous dependence.
This paper extends a theoretical model of wave attenuation through broken floating ice of random thickness to finite water depths, utilizing multiple scales analysis to derive an explicit attenuation expression that predicts an eighth-power frequency dependence at low frequencies and shows strong agreement with numerical simulations and field measurements.
This paper establishes the existence of solutions for a fully nonlinear elliptic system modeling long-range population segregation and proves their convergence to a free boundary problem with finite perimeter and semi-convex supports as the parameter vanishes.
This paper establishes the first proof of the persistence of spatial analyticity for solutions to the Majda-Biello and Hirota-Satsuma coupled KdV systems when initialized with analytic data.
This paper establishes a rigorous operator-level necessity result proving that in closed, unforced kinetic systems, the first-order Chapman-Enskog deviatoric stress arises if and only if the first-order distribution correction is nonzero, thereby filling a critical gap in the kinetic-to-continuum literature by demonstrating that vanishing precludes the emergence of stress under precise functional-analytic conditions.
This paper characterizes the second-order implicit bias of the Jordan-Kinderlehrer-Otto (JKO) scheme as a Wasserstein gradient flow on a modified energy functional that subtracts a term proportional to the squared metric curvature of the original energy, thereby explaining the scheme's unique stability and dissipation properties through its deceleration in directions of rapidly changing curvature.
This paper investigates the fractional heat equation with a Riesz potential nonlinearity, establishing a Fujita-type critical exponent that deviates from standard scaling predictions, thereby confirming a hypothesis by Mitidieri and Pohozaev and extending their nonexistence results to general convolution operators.
This paper establishes that for a generic set of finite-dimensional irreducible representations of the fundamental group of a surface's unit tangent bundle, the twisted Ruelle zeta function either vanishes at zero with an order determined by the genus or equals the Reidemeister--Turaev torsion, thereby extending Fried's conjecture to generic acyclic representations and confirming the constancy of the vanishing order for untwisted zeta functions across a dense set of Anosov metrics.
This paper establishes the existence of radial solutions with a prescribed -norm for a -Laplacian equation involving a general radial potential by employing a variational min-max argument supported by a new global boundedness result for subsolutions and a corresponding Pohozaev identity.
This paper presents an analytical pulse-response analysis of a reaction-advection-diffusion equation modeling a narrow reactor tube, demonstrating that the characteristics of a first-order irreversible reaction can be readily determined by comparing the exit flow curve with and without chemical activity.
This paper establishes the non-radial linear stability of liquid Lane-Emden stars against irrotational perturbations by proving that the associated linear operator is strictly positive whenever the radial mode is stable, despite the inability to control the gradient norm of the perturbations.
This paper addresses the ill-posed nature of kinematic differential equations in two-phase flows with discontinuous velocity fields by employing differential inclusions to rigorously define co-moving sets and prove an extended Reynolds transport theorem that accounts for phase change and interfacial slip.
This paper demonstrates the failure of unconditional uniqueness for mild solutions to the Navier-Stokes and fractional Navier-Stokes equations in Besov spaces with negative regularity by constructing non-trivial stationary singular solutions via convex integration, while simultaneously establishing uniqueness for stationary weak solutions in an endpoint critical space.
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.