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Axioms
Special Issues
Functional Differential Equations
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Functional Differential Equations

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (1 July 2015) | Viewed by 8701

Special Issue Editor

Prof. Dr. Constantin Corduneanu

E-Mail Website
Guest Editor
Department of Mathematics, University of Texas at Arlington, Box 19408, Arlington, TX 76019, USA
Interests: differential, integral and functional equations; stability, oscillations, waves; almost periodicity, generalized fourier analysis

Special Issue Information

Dear Colleagues,

After the theories of ordinary differential equations and integral equations have been consolidated (in the mid 20th Century), new types of functional or functional differential quations, or mixed type as integrodifferential equations have caught the attention of the research world.

We should mention first that the equations with deviated arguments, usually delayed, are able to describe causal phenomena, or equations involving various operators. The birth of Functional Analysis has produced new tools to investigate new types of functional equations. Notably, the fathers of Functional Analysis, such as Volterra, Radon and F. Riesz, had preoccupations in this regard. While the classical types of functional or functional differential equations have reached an advanced stage/status, the new types of equations are not yet very advanced. Extra efforts and dedication are necessary to further these relatively new theories in cases of non-classical types of functional differential equations. Attention must be directed, in both finite and infinite cases of dimensions, as required by the new applications on the horizon.

The above is the goal of this issue of our journal. Thank you for your cooperation.

Prof. Dr. Constantin Corduneanu
Guest Editor

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Keywords

  • functional differential equations;
  • classical differential equations;
  • non-classical functional differential equations;
  • related functional equations;
  • causal functional equations;
  • integral equations (Volterra, Fredholm, Hammerstein, Urysohn);
  • integrodifferential equations;
  • equations with operators or operatorial equations;
  • applications of the above

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Published Papers (2 papers)

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Research

246 KiB  
Article
On Limiting Behavior of Contaminant Transport Models in Coupled Surface and Groundwater Flows
by Vincent J. Ervin, Michaela Kubacki, William Layton, Marina Moraiti, Zhiyong Si and Catalin Trenchea
Axioms 2015, 4(4), 518-529; https://doi.org/10.3390/axioms4040518 - 6 Nov 2015
Cited by 1 | Viewed by 4288
Abstract
There has been a surge of work on models for coupling surface-water with groundwater flows which is at its core the Stokes-Darcy problem. The resulting (Stokes-Darcy) fluid velocity is important because the flow transports contaminants. The analysis of models including the transport of [...] Read more.
There has been a surge of work on models for coupling surface-water with groundwater flows which is at its core the Stokes-Darcy problem. The resulting (Stokes-Darcy) fluid velocity is important because the flow transports contaminants. The analysis of models including the transport of contaminants has, however, focused on a quasi-static Stokes-Darcy model. Herein we consider the fully evolutionary system including contaminant transport and analyze its quasi-static limits. Full article
(This article belongs to the Special Issue Functional Differential Equations)
274 KiB  
Article
Almost Periodic Solutions of Nonlinear Volterra Difference Equations with Unbounded Delay
by Yoshihiro Hamaya, Tomomi Itokazu and Kaori Saito
Axioms 2015, 4(3), 345-364; https://doi.org/10.3390/axioms4030345 - 24 Aug 2015
Cited by 1 | Viewed by 3973
Abstract
In order to obtain the conditions for the existence of periodic and almost periodic solutions of Volterra difference equations, \( x(n+1)=f(n,x(n))+\sum_{s=-\infty}^{n}F(n,s, {x(n+s)},x(n)) \), we consider certain stability properties, which are referred to as (K, \( \rho \))-weakly uniformly-asymptotic stability and (K, \( \rho [...] Read more.
In order to obtain the conditions for the existence of periodic and almost periodic solutions of Volterra difference equations, \( x(n+1)=f(n,x(n))+\sum_{s=-\infty}^{n}F(n,s, {x(n+s)},x(n)) \), we consider certain stability properties, which are referred to as (K, \( \rho \))-weakly uniformly-asymptotic stability and (K, \( \rho \))-uniformly asymptotic stability. Moreover, we discuss the relationship between the \( \rho \)-separation condition and the uniformly-asymptotic stability property in the \( \rho \) sense. Full article
(This article belongs to the Special Issue Functional Differential Equations)
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