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We investigate the existence, uniqueness, and $L^1$-contractivity of weak solutions to a porous medium equation with fractional diffusion on an evolving hypersurface. To settle the existence, we reformulate the equation as a local problem…
In this article, we give a semi-analytic expression for survival probability when particles are diffusing in an active potential well. There is no analytic solution available in the literature, due to the requirement of inverse Laplace…
We study solution techniques for an evolution equation involving second order derivative in time and the spectral fractional powers, of order $s \in (0,1)$, of symmetric, coercive, linear, elliptic, second-order operators in bounded domains…
Green's functions in Physics have proven to be a valuable tool for understanding fundamental concepts in different branches, such as electrodynamics, solid-state and many -body problems. In quantum mechanics advanced courses, Green's…
A kind of nonlocal reaction-diffusion equations on an unbounded domain containing fractional Laplacian operator is analyzed. To be precise, we prove the convergence of solutions of the equation governed by the fractional Laplacian to the…
We investigate restricted diffusion in a bounded domain towards a small partially reactive target in three- and higher-dimensional spaces. We propose a simple explicit approximation for the principal eigenvalue of the Laplace operator with…
We provide closed formulas for (unique) solutions of nonhomogeneous Dirichlet problems on balls involving any positive power $s>0$ of the Laplacian. We are able to prescribe values outside the domain and boundary data of different orders…
Single-particle resonances are crucial for exotic nuclei near and beyond the drip lines. Since the majority of nuclei are deformed, the interplay between deformation and orbital structure near threshold becomes very important and can lead…
We present the model of a diffusion-absorption process in a system which consists of two media separated by a thin partially permeable membrane. The kind of diffusion as well as the parameters of the process may be different in both media.…
Let $H(x,p)\sim H_0(x,p)+hH_1(x,p)+\cdots$ be a semi-classical Hamiltonian on $T^*{\bf R}^n$, and $\Sigma_E=\{H_0(x,p)=E\}$ a non critical energy surface. Consider $f_h$ a semi-classical distribution (the "source") microlocalized on a…
The study of fractional order differential operators is receiving renewed attention in many scientific fields. In order to accommodate researchers doing work in these areas, there is a need for highly scalable numerical methods for solving…
We study the existence of positive solutions for a parameter-dependent nonlocal boundary value problem involving a Caputo fractional derivative, which generalizes a classic thermostat model. Our approach extends previous work by considering…
Laplace's first law of errors, which states that the frequency of an error can be represented as an exponential function of the error magnitude, was overlooked for many decades but was recently shown to describe the statistical behavior of…
This paper presents a windowed Green function (WGF) method for the numerical solution of problems of elastic scattering by "locally-rough surfaces" (i.e., local perturbations of a half space), under either Dirichlet or Neumann boundary…
Integer-order differential operators were originally used to describe local and isotropic effects, in both space and time. However, in fields like biology, the modelling of complex phenomena with spatial heterogeneity necessitates more…
Recently, a semiclassical approach to diffraction has been proposed, which treats the proton as a classical colour field. The present paper demonstrates that this approach is consistent with the concept of diffractive parton distributions.…
This paper provides a new numerical strategy to solve fractional in space reaction-diffusion equations on bounded domains under homogeneous Dirichlet boundary conditions. Using the matrix transform method the fractional Laplacian operator…
A well known description of superradiance from pointlike collections of many atoms involves the dissipative motion of a large spin. The pertinent ``superradiance master equation'' allows for a formally exact solution which we subject to a…
A formulation of the boundary integral method for solving partial differential equations has been developed whereby the usual weakly singular integral and the Cauchy principal value integral can be removed analytically. The broad…
We study classical particles on the sites of an open chain which diffuse, coagulate and decoagulate preferentially in one direction. The master equation is expressed in terms of a spin one-half Hamiltonian $H$ and the model is shown to be…