arXiv subjects

Yousef Alamri

Publications and source records attributed to Yousef Alamri.

3 recordsLinked to original sources

arXiv2026

The two-phase Alt-Phillips problem for quasilinear operators

We establish interior regularity and optimal growth estimates for sign-changing minimizers of the $p-$singular or $p-$degenerate quasilinear Alt--Phillips functional throughout the full range of $1<p<\infty$ and of the nonlinearity power $0<\gamma<p$. In addition, we obtain local finite perimeter and density estimates, from which we deduce the local $(N-1)$-rectifiability of the reduced and two-phase free boundaries and the local finiteness of their $(N-1)$-dimensional Hausdorff measure for a restricted range of $\gamma$.

math.AP↗

arXiv2025

Aggregation-Confinement-Diffusion Evolutions with Saturation: Regularity and Long-Time Asymptotics

We establish Hölder regularity for the weak solution to a degenerate diffusion equation in the presence of a local (drift) potential and nonlocal (interaction) term, posed in a bounded domain with no-flux boundary conditions. The degeneracy is due to saturation, i.e., it occurs when the solution reaches its maximal value. As a byproduct of the established regularity and the underlying dissipative structure of the evolution, we prove the uniform convergence of contractive solutions to a stationary state as $t \to \infty$.

math.AP↗

arXiv2023

Very High-Order A-stable Stiffly Accurate Diagonally Implicit Runge-Kutta Methods with Error Estimators

A numerical search approach is used to design high-order diagonally implicit Runge-Kutta (DIRK) schemes equipped with embedded error estimators, some of which have identical diagonal elements (SDIRK) and explicit first stage (ESDIRK). In each of these classes, we present new A-stable schemes of order six (the highest order of previously known A-stable DIRK-type schemes) up to order eight. For each order, we include one scheme that is only A-stable as well as schemes that are L-stable, stiffly accurate, and/or have stage order two. The latter types require more stages, but give better convergence rates for differential-algebraic equations (DAEs), and those which have stage order two give better accuracy for moderately stiff problems. The development of the eighth-order schemes requires, in addition to imposing A-stability, finding highly accurate numerical solutions for a system of 200 equations in over 100 variables, which is accomplished via a combination of global and local optimization strategies. The accuracy, stability, and adaptive stepsize control of the schemes are demonstrated on diverse problems.

math.NA↗