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This https://arxiv.org/abs/2505.04316 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

On local fields invariant under the action of topological defects
In the context of rational conformal field theories (RCFT) we look into the problem of constructing and classifying pairs consisting of a local operator and a topological defect which commutes or anticommutes with it. We discuss the bulk and boundary versions of the problem. In the latter one considers a conformal boundary condition, a boundary operator on it and a junction with a topological defect. In the case of the charge conjugation modular invariant commuting configurations in each proble…

This https://arxiv.org/abs/2505.23679 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Boundary terms in cosmology
In the derivation of the Einstein field equations via Hamilton's principle, the inclusion of a boundary term is essential to render the variational problem well-posed, as it addresses variations that do not vanish at the boundary of the spacetime manifold. Typically, this term is chosen as the Gibbons-Hawking-York boundary term. In this work, we propose an alternative treatment of the boundary term within a cosmological framework by employing the Lagrange multiplier method. This approach enforc…

Change of bifurcation type in 2D free boundary model of a moving cell with nonlinear diffusion
Leonid Berlyand, Oleksii Krupchytskyi, Tim Laux
https://arxiv.org/abs/2506.03138

Change of bifurcation type in 2D free boundary model of a moving cell with nonlinear diffusion
We introduce a 2D free boundary problem with nonlinear diffusion that models a living cell moving on a substrate. We prove that this nonlinearity results in a qualitative of solution behavior compared to the linear diffusion case (Rybalko et al. TAMS 2023), namely the switch between direct and inverse pitchfork bifurcation. Our objectives are twofold: (i) develop a rigorous framework to prove existence of bifurcation and determining its type (subcritical vs. superctitical) and (ii) the deri…

Boundary bilinear control of semilinear parabolic PDEs: quadratic convergence of the SQP method
Eduardo Casas, Mariano Mateos
https://arxiv.org/abs/2505.24237

Boundary bilinear control of semilinear parabolic PDEs: quadratic convergence of the SQP method
We analyze a bilinear control problem governed by a semilinear parabolic equation. The control variable is the Robin coefficient on the boundary. First-order necessary and second-order sufficient optimality conditions are derived. A sequential quadratic programming algorithm is then proposed to compute local solutions. Starting the iterations from an initial point in an $L^2$-neighborhood of the local solution we prove stability and quadratic convergence of the algorithm in $L^p$ ($p < \infty$)…

Numerical methods for fully nonlinear degenerate diffusions
Edgard A. Pimentel, Erc\'ilia Sousa
https://arxiv.org/abs/2506.02595 https://

Numerical methods for fully nonlinear degenerate diffusions
We propose finite difference methods for degenerate fully nonlinear elliptic equations and prove the convergence of the schemes. Our focus is on the pure equation and a related free boundary problem of transmission type. The cornerstone of our argument is a regularisation procedure. It decouples the degeneracy term from the elliptic operator driving the diffusion process. In the free boundary setting, the absence of degenerate ellipticity entails new, genuine difficulties. To bypass them, we re…

Laser-plasma acceleration in a conical plasma channel with longitudinally inhomogeneous plasma profile
D. S. Bondar, W. Leemans, V. I. Maslov, I. N. Onishchenko
https://arxiv.org/abs/2506.04021

Laser-plasma acceleration in a conical plasma channel with longitudinally inhomogeneous plasma profile
Laser-plasma acceleration is considered as a modern method of accelerating bunches using a wakefield excited by a laser pulse. This paper demonstrates the use of a longitudinally inhomogeneous increasing plasma density gradient in a conical channel to increase of the energy of a self-injected bunch. Comparison of a conical channels with homogeneous and inhomogeneous plasma and also conical and cylindrical homogeneous channels, shows a clear advantage of an inhomogeneous conical channel. The lon…

The Boundary Reproduction Number for Determining Boundary Steady State Stability in Chemical Reaction Systems
Matthew D. Johnston, Florin Avram
https://arxiv.org/abs/2506.01606

The Boundary Reproduction Number for Determining Boundary Steady State Stability in Chemical Reaction Systems
We introduce the boundary reproduction number, adapted from the next generation matrix method, to assess whether an infusion of species will persist or become exhausted in a chemical reaction system. Our main contributions are as follows: (a) we show how the concept of a siphon, prevalent in Petri nets and chemical reaction network theory, identifies sets of species that may become depleted at steady state, analogous to a disease-free boundary steady state; (b) we develop an approach for incorp…

Boundary H\"older gradient estimates for parabolic $p$-Laplace type equations
Se-Chan Lee, Yuanyuan Lian, Hyungsung Yun, Kai Zhang
https://arxiv.org/abs/2506.01018

Boundary Hölder gradient estimates for parabolic $p$-Laplace type equations
In this paper, we study the boundary regularity for viscosity solutions of parabolic $p$-Laplace type equations. In particular, we obtain the boundary pointwise $C^{1,α}$ regularity and global $C^{1,α}$ regularity.

Point Jacobi-type preconditioning and parameter tuning for Calderon-preconditioned Burton-Miller method in transmission problems
Keigo Tomoyasu, Hiroshi Isakari
https://arxiv.org/abs/2506.01440

Point Jacobi-type preconditioning and parameter tuning for Calderon-preconditioned Burton-Miller method in transmission problems
It was recently demonstrated that the boundary element method based on the Burton-Miller formulation (BM-BEM), widely used for solving exterior problems, can be adapted to solve transmission problems efficiently. This approach utilises Calderon's identities to improve the spectral properties of the underlying integral operator. Consequently, most eigenvalues of the squared BEM coefficient matrix, i.e. the collocation-discretised version of the operator, cluster at a few points in the complex pl…

This https://arxiv.org/abs/2408.05197 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Inverse Iteration for the Laplace Eigenvalue Problem with Robin and Mixed Boundary Conditions
We apply the method of inverse iteration to the Laplace eigenvalue problem with Robin and mixed Dirichlet-Neumann boundary conditions, respectively. For each problem, we prove convergence of the iterates to a non-trivial principal eigenfunction and show that the corresponding Rayleigh quotients converge to the principal eigenvalue. We also propose a related iterative method for an eigenvalue problem arising from a model for optimal insulation and provide some partial results.