Related papers: A sharp error estimate of piecewise polynomial col…

Second-order methods are of great importance for composite convex optimization problems due to their local super-linear convergence rates (under appropriate assumptions). However, the presence of even a simple nonsmooth function in the…

The global-in-time existence of weak solutions to a spatially homogeneous multispecies Fokker-Planck-Landau system for plasmas in the three-dimensional whole space is shown. The Fokker-Planck-Landau system is a simplification of the Landau…

We present a theoretical and computational framework based on fractional calculus for the analysis of the nonlocal static response of cylindrical shell panels. The differ-integral nature of fractional derivatives allows an efficient and…

This paper studies the Sobolev regularity estimates for weak solutions of a class of degenerate, and singular quasi-linear elliptic problems of the form $\text{div}[\mathbf{A}(x,u, \nabla u)]= \text{div}[\mathbf{F}]$ with non-homogeneous…

The next-to-next-to-leading order (NNLO) pQCD correction to the inclusive decays of the heavy quarkonium $\eta_Q$ ($Q$ being $c$ or $b$) has been done in the literature within the framework of nonrelativistic QCD. One may observe that the…

As in the case of soliton PDEs in 2+1 dimensions, the evolutionary form of integrable dispersionless multidimensional PDEs is non-local, and the proper choice of integration constants should be the one dictated by the associated Inverse…

We study the problem of minimizing a $m$-weakly convex and possibly nonsmooth function. Weak convexity provides a broad framework that subsumes convex, smooth, and many composite nonconvex functions. In this work, we propose a…

Many local integral methods are based on an integral formulation over small and heavilly overlapping stencils with local RBF interpolations. These functions have become an extremely effective tool for interpolation on scattered node sets,…

In the paper titled "New numerical approach for fractional differential equations" by A. Atangana and K.M. Owolabi [Math. Model. Nat. Phenom., 13(1), 2018], it is presented a method for the numerical solution of some fractional differential…

We enumerate the local Petrovskii lacunas (that is, the domains of local regularity of the principal fundamental solutions) of strictly hyperbolic PDE's with constant coefficients in $R^N$ at the parabolic singular points of their…

This article deals with the convergence of finite volume scheme (FVS) for solving coagulation and multiple fragmentation equations having locally bounded coagulation kernel but singularity near the origin due to fragmentation rates. Thanks…

In this paper, we study solutions for a weakly coupled system of eikonal equations arising in an optimal path-planning problem with random breakdown. The model considered takes into account two types of breakdown for the vehicle, partial…

We propose and study a class of numerical schemes to approximate time fractional differential equations. The methods are based on the approximation of the Caputo fractional derivative by continuous piecewise polynomials, which is strongly…

Consider the scattering of time-harmonic point sources by an infinite locally rough interface with bounded obstacles embedded in the lower half-space. The model problem is first reduced to an equivalent integral equation formulation defined…

This work presents a collocation method for solving linear Fredholm integral equations of the second kind defined on a closed contour in the complex plane. The right-hand side of the equation is a piecewise continuous function that may have…

We study the Boltzmann equation with the constant collision kernel in the case of spatially periodic domain $\mathbb{T}^d$, $d\geq 2$. Using the existing techniques from nonlinear dispersive PDEs, we prove the local well-posedness result in…

It is shown that $u_k \cdot v_k$ converges weakly to $u\cdot v$ if $u_k\weakto u$ weakly in $L^p$ and $v_k\weakly v$ weakly in $L^q$ with $p, q\in (1,\infty)$, $1/p+1/q=1$, under the additional assumptions that the sequences $\Div u_k$ and…

Many practical optimization problems lack strong convexity. Fortunately, recent studies have revealed that first-order algorithms also enjoy linear convergences under various weaker regularity conditions. While the relationship among…

We propose a physics-informed machine learning method for uncertainty quantification in high-dimensional inverse problems. In this method, the states and parameters of partial differential equations (PDEs) are approximated with truncated…

The polar coordinate transformation (PCT) method has been extensively used to treat various singular integrals in the boundary element method (BEM). However, the resultant integrands of the PCT tend to become nearly singular when (1) the…