On a class of PDEs with nonlinear distributed in space and time state-dependent delay term

2006/11/21 by Alexander V. Rezounenko, Rezounenko, Alexander V.
Computer Science · Engineering · Mathematics · #35B41 #35K57 #35R10 #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.math/0611653

openalex publication_date 2006/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A new class of nonlinear partial differential equations with distributed in space and time state-dependent delay is investigated. We find appropriate assumptions on the kernel function which represents the state-dependent delay and discuss advantages of this class. Local and long-time asymptotic properties, including the existence of global attractor, are studied.

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