Search results for "Differential equation"
showing 10 items of 759 documents
Derivation of a Homogenized Two-Temperature Model from the Heat Equation
2014
This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential equations governing the evolution of the temperature of each phase at a macroscopic level of description. The coupling terms describing the exchange of heat between the phases are obtained by using homogenization techniques originating from [D. Cioranescu, F. Murat: Coll\`ege de France Seminar vol. 2. (Paris 1979-1980) Res. Notes in Math. vol. 60, pp. 98-138. Pitman, Boston, London, 1982.]
On asymptotic behavior of solutions to higher-order sublinear Emden–Fowler delay differential equations
2017
Abstract We study asymptotic behavior of solutions to a class of higher-order sublinear Emden–Fowler delay differential equations. Our theorems improve several results reported recently in the literature. Two examples are provided to illustrate the importance and advantages of new criteria.
Elliptic equations and maps of bounded length distortion
1988
On considere l'equation elliptique d'ordre 2: L(u)=Σ i,f=1 n ∂ 1 (a ij ∂ ju )=0 ou les coefficients a ij sont des fonctions C 1 dans un domaine D de R n
Multiple Solutions for Fractional Boundary Value Problems
2018
Variational methods and critical point theorems are used to discuss existence and multiplicity of solutions for fractional boundary value problem where Riemann–Liouville fractional derivatives and Caputo fractional derivatives are used. Some conditions to determinate nonnegative solutions are presented. An example is given to illustrate our results.
On the solution of a parabolic PDE involving a gas flow through a semi-infinite porous medium
2021
Abstract Taking as start point the parabolic partial differential equation with the respective initial and boundary conditions, the present research focuses onto the flow of a sample of waste-water derived from a standard/conventional dyeing process. In terms of a highly prioritized concern, meaning environment decontamination and protection, in order to remove the dyes from the waste waters, photocatalyses like ZnO or TiO2 nanoparticles were formulated, due to their high surface energy which makes them extremely reactive and attractive. According to the basics of ideal fluid, the key point is the gas flow through an ideal porous pipe consisting of nanoparticles bound one to each other, for…
THE GYROTRON STARTUP SCENARIO IN THE SINGLE MODE TIME DEPENDENT APPROACH
2019
The paper explains how to solve the Gyrotron equation system in the Single Mode Time Dependent Approach. In particular, we point out problems encountered when solving these well-known equations. The starting current estimation approach a using time model is suggested. The solution has been implemented in the Matlab code, which is attached to the article.
Stochastic models for phytoplankton dynamics in Mediterranean Sea
2016
Abstract In this paper, we review some results obtained from three one-dimensional stochastic models, which were used to analyze picophytoplankton dynamics in two sites of the Mediterranean Sea. Firstly, we present a stochastic advection–reaction–diffusion model to describe the vertical spatial distribution of picoeukaryotes in a site of the Sicily Channel. The second model, which is an extended version of the first one, is used to obtain the vertical stationary profiles of two groups of picophytoplankton, i.e. Pelagophytes and Prochlorococcus, in the same marine site as in the previous case. Here, we include intraspecific competition of picophytoplanktonic groups for limiting factors, i.e.…
Accounting for preferential sampling in species distribution models
2019
D. C., A. L. Q. and F. M. would like to thank the Ministerio de Educación y Ciencia (Spain) for financial support (jointly financed by the European Regional Development Fund) via Research Grants MTM2013‐42323‐P and MTM2016‐77501‐P, and ACOMP/2015/202 from Generalitat Valenciana (Spain). Species distribution models (SDMs) are now being widely used in ecology for management and conservation purposes across terrestrial, freshwater, and marine realms. The increasing interest in SDMs has drawn the attention of ecologists to spatial models and, in particular, to geostatistical models, which are used to associate observations of species occurrence or abundance with environmental covariates in a fi…
Sliding solutions of second-order differential equations with discontinuous right-hand side
2017
We consider second-order ordinary differential equations with discontinuous right-hand side. We analyze the concept of solution of this kind of equations and determine analytical conditions that are satisfied by typical solutions. Moreover, the existence and uniqueness of solutions and sliding solutions are studied. Copyright © 2017 John Wiley & Sons, Ltd.
Crowd-Averse Robust Mean-Field Games: Approximation via State Space Extension
2016
We consider a population of dynamic agents, also referred to as players. The state of each player evolves according to a linear stochastic differential equation driven by a Brownian motion and under the influence of a control and an adversarial disturbance. Every player minimizes a cost functional which involves quadratic terms on state and control plus a cross-coupling mean-field term measuring the congestion resulting from the collective behavior, which motivates the term “crowd-averse.” Motivations for this model are analyzed and discussed in three main contexts: a stock market application, a production engineering example, and a dynamic demand management problem in power systems. For th…