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On average population levels for models with directed diffusion in heterogeneous environments

This paper investigates the total population levels in heterogeneous environments with directed diffusion for any power-law relationship between intrinsic growth rate and carrying capacity, disproving the existence of a critical exponent that determines population prevalence over carrying capacity and analyzing how the total population depends on the diffusion coefficient under a generalized dispersal strategy.

André Rickes, Elena Braverman2026-03-06🔢 math

Stability and bifurcation analysis in a mechanochemical model of pattern formation

This paper analyzes a mechanochemical model of pattern formation in regenerating tissue spheroids, demonstrating that a feedback loop between mechanical stretching and morphogen production, coupled with global strain conservation, robustly generates stable single-peaked patterns through specific bifurcation structures without requiring a second diffusible inhibitor.

Szymon Cygan, Anna Marciniak-Czochra, Finn Münnich + 1 more2026-03-06🔢 math

Quantitative stability for quasilinear parabolic equations

This paper establishes explicit quantitative convergence rates for viscosity solutions of quasilinear parabolic equations under perturbations, including variations in the exponent $p$ and regularized approximations, by adapting standard comparison arguments to cover both singular and degenerate cases like the normalized and variational $p$ -parabolic equations.

Tapio Kurkinen, Qing Liu2026-03-06🔢 math

Quantitative entropy estimates for 2D stochastic vortex model on the whole space under moderate interactions

This paper establishes quantitative pathwise entropy bounds for a stochastic 2D vortex model on the whole space under moderate interactions by combining Donsker-Varadhan inequalities with localization techniques, and subsequently derives new energy estimates for the convergence of particle systems to the limiting process.

Alexandre B. de Souza2026-03-06🔢 math

The regularity of the boundary of vortex patches for the quasi-geostrophic shallow-water equations

This paper establishes the persistence of boundary smoothness for vortex patches in the quasi-geostrophic shallow-water equations and demonstrates their local-in-time convergence to Euler solutions as the Rossby radius parameter tends to zero.

Marc Magaña, Joan Mateu, Joan Orobitg2026-03-06🔢 math

Construction of infinite time bubble tower solutions to critical wave maps equation

This paper establishes the existence of global-in-time, $k$ -corotational wave map solutions that asymptotically decompose into an arbitrary number of alternating-sign concentric bubbles with vanishing radiation, utilizing a backward construction method and a novel Morawetz-type functional to prove the soliton resolution conjecture for $k \geq 3$ .

Seunghwan Hwang, Kihyun Kim2026-03-06🔢 math

Sharp remainder formulae for general weighted Hardy and Rellich type inequalities for $1<p<\infty$

This paper extends the weighted $L^p$ -Hardy inequalities and identities to the full range $1<p<\infty $, while also establishing a new sharp remainder formula for general weighted$ L^p$-Rellich inequalities involving quasilinear second-order degenerate elliptic operators.

Yerkin Shaimerdenov, Nurgissa Yessirkegenov, Amir Zhangirbayev2026-03-06🔢 math

Well-posedness and mean-field limit of discontinuous weighted dynamics via the relative entropy method

This paper establishes the well-posedness of deterministic particle dynamics with time-evolving weights and their associated Kolmogorov and mean-field equations under mild regularity assumptions, utilizing entropy estimates and the relative entropy method to rigorously derive the mean-field limit.

Immanuel Ben Porat, José A. Carrillo, Alexandra Holzinger2026-03-06🔢 math

Upper bounds of nodal sets for solutions of bi-Laplace equations: II

This paper establishes a polynomial upper bound for the nodal sets of solutions to bi-Laplace equations by deriving delicate monotonicity and propagation of smallness results via Carleman estimates, thereby avoiding the use of frequency functions central to Logunov's work.

Jiuyi Zhu2026-03-06🔢 math

The Asymptotic Behaviour of Oldroyd-B Fluids is Almost Newtonian

This paper demonstrates that for Oldroyd-B viscoelastic fluids, the stress tensor and elastic components decay at rates that cause the fluid to exhibit almost Newtonian behavior over large time scales, as the elastic part vanishes faster than the Newtonian deformation.

Matthias Hieber, Thieu Huy Nguyen, César J. Niche + 1 more2026-03-06🔢 math

Potential Theory of the Fractional-Logarithmic Laplacian: Global Regularity and Critical Compact Embeddings

This paper establishes a comprehensive potential-theoretic framework for the fractional-logarithmic Laplacian by deriving explicit kernel representations and sharp asymptotics, defining associated logarithmic Bessel spaces, and proving global regularity results alongside critical compact embeddings that exhibit a strict logarithmic gain.

Rui Chen2026-03-06🔢 math

Multi-Species Keller--Segel Systems: Analysis, Pattern Formation, and Emerging Mathematical Structures

This article provides a comprehensive survey of multi-species Keller--Segel systems, synthesizing classical and recent results on their analytical well-posedness, blow-up mechanisms, and pattern formation dynamics to clarify the structural principles governing complex chemotactic interactions in biological and ecological contexts.

Kolade M Owolabi, Eben Mare, Clara O Ijalana + 1 more2026-03-06🔢 math

$\mathrm{L}^{2}$ --convergence of the time-splitting scheme for nonlinear Dirac equation in 1+1 dimensions

This paper proves the $\mathrm{L}^{2}$ -convergence of the time-splitting scheme to the unique global strong solution of the nonlinear Dirac equation in 1+1 dimensions by establishing pointwise estimates, constructing a modified Glimm-type functional for stability, and demonstrating the precompactness of the approximate solutions.

Ningning Li, Yongqian Zhang, Qin Zhao2026-03-06🔢 math

Limiting absorption principle for time-harmonic acoustic and electromagnetic scattering of plane waves from a bi-periodic inhomogeneous layer

This paper establishes the Limiting Absorption Principle for time-harmonic acoustic and electromagnetic scattering from bi-periodic inhomogeneous layers supporting Bound States in the Continuum, thereby deriving a sharp radiation condition that ensures solution uniqueness by combining the classical Rayleigh expansion with a newly proven orthogonal identity.

Guanghui Hu, Andreas Kirsch, Yulong Zhong2026-03-06🔢 math

Regularization by noise for Gevrey well-posedeness of a weakly hyperbolic operator

This paper demonstrates that a suitable multiplicative Stratonovich noise perturbation can restore $C^{\infty}$ well-posedness to the Cauchy problem of a weakly hyperbolic operator with double involutive characteristics, whereas its deterministic counterpart is restricted to well-posedness only within Gevrey classes $1 \leq s < 2$.

Enrico Bernardi, Alberto Lanconelli2026-03-06🔢 math

Boundary stabilization of flows in networks of open channels modeled by Saint-Venant equations

This paper establishes the boundary stabilization of flows in star-shaped and tree-shaped open channel networks governed by Saint-Venant equations with friction by constructing a novel explicit Lyapunov function that enables optimal control using only terminal node actuators, even in the absence of internal controls.

Amaury Hayat, Yating Hu, Peipei Shang2026-03-06🔢 math

Dispersion for the Schr{ö}dinger equation on the line with short-range array of delta potentials

This paper establishes the $L^1(\mathbb{R}) \to L^\infty(\mathbb{R})$ dispersive estimate with a decay rate of $|t|^{-1/2}$ for the one-dimensional Schrödinger equation perturbed by a short-range array of delta potentials, provided the coupling constants decay sufficiently and no zero-energy resonance exists.

Romain Duboscq, Élio Durand-Simonnet, Stefan Le Coz2026-03-06🔢 math

Regularization of the superposition principle: Potential theory meets Fokker-Planck equations

This paper advances the superposition principle for Fokker-Planck equations by constructing a full-fledged right Markov process under general measurability conditions, thereby resolving the open problem of establishing the strong Markov property and enabling new probabilistic solutions to the parabolic Dirichlet problem and flow constructions for both linear and nonlinear cases, including the generalized porous media equation.

Lucian Beznea, Iulian Cîmpean, Michael Röckner2026-03-06🔢 math

Besov regularity of solutions to the Dirichlet problem for the Bessel $(p,s)$ -Laplacian

This paper establishes global Besov regularity estimates for weak solutions to the Dirichlet problem of a fractional $p$ -Laplacian defined via the Riesz fractional gradient by combining Lions-Calderón spaces, Besov embeddings, and an adapted Nirenberg difference quotient method, yielding specific regularity indices that depend on the interplay between the order $s$ and the exponent $p$ in both superquadratic and subquadratic regimes.

Juan Pablo Borthagaray, Leandro M. Del Pezzo, José Camilo Rueda Niño2026-03-06🔢 math

The Extra Vanishing Structure and Nonlinear Stability of Multi-Dimensional Rarefaction Waves: The Geometric Weighted Energy Estimates

This paper establishes the nonlinear stability of multi-dimensional rarefaction waves for the compressible Euler equations by introducing a novel Geometric Weighted Energy Method that overcomes derivative loss issues through the identification of a hidden vanishing structure in the top-order derivatives of the characteristic speed.

Haoran He, Qichen He2026-03-06🔬 physics

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