Partial differential equations with discrete and distributed state-dependent delays

By A. Rezounenko. 2005

69 citations recorded by the source corpus.

This work is an attempt to treat partial differential equations with discrete (concentrated) state-dependent delay. The main idea is to approximate the discrete delay term by a sequence of distributed delay terms (all with state-dependent delays). We study local existence and long-time asymptotic behavior of solutions and prove that the model with distributed delay has a global attractor while the one with discrete delay possesses the trajectory attractor.

Subfields: Computational Theory and Mathematics, Computer Networks and Communications, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/2d61dbeda01a4b09b175119c67d854fec038552b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. E. Hernández
2. E. Hernández M.
3. Rathinasamy Sakthivel
4. A. Rezounenko

In Computer Networks and Communications

1. A. Rezounenko
2. Ferenc Hartung
3. Tibor Krisztin

In Control and Systems Engineering

1. A. Dinesh Kumar Anguraj
2. E. Hernández
3. E. Hernández M.
4. Rathinasamy Sakthivel
5. A. Rezounenko
6. Zuomao Yan
7. Ferenc Hartung
8. Hongwu Zhang

Citations in the corpus

• Existence results for impulsive evolution differential equations with state-dependent delay. (2008, background): “There exists a extensive literature for ordinary state-dependent delay equations, see among another works, [2, 1, 3, 4, 6, 7, 8]. The study of partial dierential equations with state dependent delay have been initiated recently, and concerning this matter we cite the pioneer works Rezounenko et al. ”
• Existence results for an impulsive neutral functional differential equation with state-dependent delay (2007, background): “The literature related to partial functional differential equations with state dependent delay is very recent and limited, to our knowledge, to the works 3 , 20–22 , 33 .”
• Differential equations with discrete state-dependent delay: Uniqueness and well-posedness in the space of continuous functions (2008, methodology): “The existence (without uniqueness) of solutions for P.D.E.s with discrete state-dependent delay was studied in [Hernandez et al (2006)] (mild solutions) and [Rezounenko (2007)] (weak solutions).”