Search results for " Differential equations"

Global integrability of the gradients of solutions to partial differential equations

1994

On ordinary differential equations with interface conditions

1968

Linear Systems Excited by Polynomials of Filtered Poission Pulses

1997

The stochastic differential equations for quasi-linear systems excited by parametric non-normal Poisson white noise are derived. Then it is shown that the class of memoryless transformation of filtered non-normal delta correlated process can be reduced, by means of some transformation, to quasi-linear systems. The latter, being excited by parametric excitations, are frst converted into ltoˆ stochastic differential equations, by adding the hierarchy of corrective terms which account for the nonnormality of the input, then by applying the Itoˆ differential rule, the moment equations have been derived. It is shown that the moment equations constitute a linear finite set of differential equatio…

Modeling of surface structure formation after laser irradiation

2011

The Stefan problem in a semi-infinite media under laser irradiation is considered. It is related to the melting and solidification processes, resulting in certain surface structure after the solidification. A simple model, as well as a more sophisticated one is proposed to describe this process. The latter model allows us to calculate the surface profile by solving a system of two nonlinear differential equations, if the shape of the solid-liquid interface is known. It has to be found as a solution of two-phases Stefan problem. The results of example calculations by the fourth-order Runge-Kutta method are presented, assuming that the solid-liquid interface has a parabolic shape. The calcula…

A best proximity point approach to existence of solutions for a system of ordinary differential equations

2019

We establish the existence of a solution for the following system of differential equations (y x ′′((t t ) ) = = g f ((t t ,y x ((t t )) )) ,y x ((t t 0 0) ) = = x x *** in the space of all bounded and continuous real functions on [0, +∞[. We use best proximity point methods and measure of noncompactness theory under suitable assumptions on f and g. Some new best proximity point theorems play a key role in the above result.

epiModel: A system to build automatically systems of differential equations of compartmental type-epidemiological models

2011

In this paper we describe epiModel, a code developed in Mathematica that facilitates the building of systems of differential equations corresponding to type-epidemiological linear or quadratic models whose characteristics are defined in text files following an easy syntax. It includes the possibility of obtaining the equations of models involving age and/or sex groups. © 2011.

A model of oil burnout from glass fabric

1997

A mathematical model is proposed for the process of the removal (by burning) of oil contained in a glass fibre insulation fabric manufactured in Latvia. The small aspect ratio of the fabric allows simplifications to the modelling which reduce the problem to a single nonlinear ordinary differential equation. When the effects of reflected radiation are also included, the differential equation is supplemented by two integral equations. Predictions of the position of the ‘burning zone’ accord well with observations made at the factory. The effect of the inclusion of extra heating chambers is also examined, and it is found that the temperature gradient in the fabric may be greatly decreased in t…

Solutions to the 1-harmonic flow with values into a hyper-octant of the N-sphere

2013

Abstract We announce existence results for the 1-harmonic flow from a domain of R m into the first hyper-octant of the N -dimensional unit sphere, under homogeneous Neumann boundary conditions. The arguments rely on a notion of “geodesic representative” of a BV-vector field on its jump set.

THE 1-HARMONIC FLOW WITH VALUES IN A HYPEROCTANT OF THE N-SPHERE

2014

We prove the existence of solutions to the 1-harmonic flow — that is, the formal gradient flow of the total variation of a vector field with respect to the [math] -distance — from a domain of [math] into a hyperoctant of the [math] -dimensional unit sphere, [math] , under homogeneous Neumann boundary conditions. In particular, we characterize the lower-order term appearing in the Euler–Lagrange formulation in terms of the “geodesic representative” of a BV-director field on its jump set. Such characterization relies on a lower semicontinuity argument which leads to a nontrivial and nonconvex minimization problem: to find a shortest path between two points on [math] with respect to a metric w…

Approximate analytic and numerical solutions to Lane-Emden equation via fuzzy modeling method

2012

Published version in the journal: Mathematical Problems in Engineering. Also available from the publisher: http://dx.doi.org/10.1155/2012/259494 A novel algorithm, called variable weight fuzzy marginal linearization VWFML method, is proposed. Thismethod can supply approximate analytic and numerical solutions to Lane-Emden equations. And it is easy to be implemented and extended for solving other nonlinear differential equations. Numerical examples are included to demonstrate the validity and applicability of the developed technique.