相关论文: A new approach to the Thomas-Fermi boundary-value …

This article proves the well posedness of the boundary value problemthat arises when PML algorithms are applied to Pauli's equationswith a three dimensional rectangle as computational domain. The absorptionsare positive near the boundary…

We investigate the Cauchy problem for a semilinear spatio--temporal fractional diffusion equation with a time-dependent forcing term: \[ \partial_t^\alpha u + (-\Delta)^{\mathsf{s}} u = |u|^p + t^{\sigma}\,\mathbf{w}(x), \quad (t,x) \in…

The Majorana transformation makes it possible to reduce the Thomas-Fermi equation to a first-order differential equation. This reduction is possible due to the special scaling property of the Thomas-Fermi equation under homology…

Boundary conditions effects are explored for size-dependent models in thermal equilibrium. Scalar and fermionic models are used for $D=1+3$ (films), $D=1+2$ (hollow cylinder) and $D=1+1$ (ring). For all models a minimal length is found,…

We show that a simple and straightforward rational approximation to the Thomas--Fermi equation provides the slope at origin with unprecedented accuracy. We compare present approach with other available ones.

We consider the initial boundary value problem \begin{eqnarray*}u_t=\mu u_x+\tfrac{1}{2}u_{xx}\qquad (t>0,x\ge0),\\u(0,x)=f(x)\qquad (x\ge0),\\u_t(t,0)=\nu u_x(t,0)\qquad (t>0)\end{eqnarray*} of Stroock and Williams [Comm. Pure Appl. Math.…

We present a new semiclassical theory for describing pairing in finite Fermi systems. It is based on taking the $\hbar \to 0$, i.e. Thomas-Fermi, limit of the gap equation written in the basis of the mean field (weak coupling). In addition…

We study boundary value problems associated with singular, strongly nonlinear differential equations with functional terms of type $$\big(\Phi(k(t)\,x'(t))\big)' + f(t,\mathcal{G}_x(t))\,\rho(t, x'(t)) = 0$$ on a compact interval $[a,b]$.…

A non-classical initial and boundary value problem for a non-homogeneous one-dimensional heat equation for a semi-infinite material with a zero temperature boundary condition at the face $x=0$ is studied with the aim of finding explicit…

We consider the Helmholtz equation defined in unbounded domains, external to 2D bounded ones, endowed with a Dirichlet condition on the boundary and the Sommerfeld radiation condition at infinity. To solve it, we reduce the infinite region,…

Recently it was obtained in [Tarzia, Thermal Sci. 21A (2017) 1-11] for the classical two-phase Lam\'e-Clapeyron-Stefan problem an equivalence between the temperature and convective boundary conditions at the fixed face under a certain…

We justify the Thomas--Fermi approximation for the elliptic problem with the repulsive nonlinear confinement used in the recent physical literature. The method is based on the resolvent estimates and the fixed-point iterations.

We construct approximate solutions to the time--dependent Schr\"odinger equation $i \hbar (\partial \psi)/(\partial t) = - (\hbar^2)/2 \Delta \psi + V \psi$ for small values of $\hbar$. If $V$ satisfies appropriate analyticity and growth…

Using Leray-Schauder degree or degree for $\alpha$-condensing maps we obtain the existence of at least one solution for the boundary value problem of the type \[ \left\{\begin{array}{lll} (\varphi(u' ))' = f(t,u,u') & & \\ u(T)=0=u'(0), & &…

The momentous objective of this work is to discuss some qualitative properties of solutions such as the estimate on the solutions, the continuous dependence of the solutions on initial conditions as well as the existence and uniqueness of…

This paper is concerned with the blowup phenomena for initial-boundary value problem for certain semi linear parabolic, dispersive and hyperbolic equations in cone-like domain. The result proposes a unified treatment of estimates for…

We provide very effective methods to convert both asymptotic and explicit numeric bounds on the prime counting function $\psi(x)$ to bounds of the same type on both $\theta(x)$ and $\pi(x)$. This follows up our previous work on $\psi(x)$ in…

The model under consideration is based on approximate analytical solution of two dimensional stationary Navier-Stokes and Fourier-Kirchhoff equations. Approximations are based on the typical for natural convection assumptions: the fluid…

We analyze the fundamental solution of a time-fractional problem, establishing existence and uniqueness in an appropriate functional space. We also focus on the one-dimensional spatial setting in the case in which the time-fractional…

We consider a boundary value problem involving conformable derivative of order $\alpha ,$ $1<\alpha <2$ and Dirichlet conditions. To prove the existence of solutions, we apply the method of upper and lower solutions together with Schauder's…