Parabolic Differential Equations with Bounded Delay

2022/07/18 by Marek Kryspin, Kryspin, Marek, Janusz Mierczyński +1 · 1 citation
Computer Science · Engineering · Mathematics · #35A01 #35K15 #35R10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #Dynamical Systems (math.DS) #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2207.08516

openalex publication_date 2022/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show the continuous dependence of solutions of linear nonautonomous second order parabolic partial differential equations (PDEs) with bounded delay on coefficients and delay. The assumptions are very weak: only convergence in the weak-* topology of delay coefficients is required. The results are important in the applications of the theory of Lyapunov exponents to the investigation of PDEs with delay.

Cited by

• Weighted well-posedness and kernel stability for coercive evolution equations with measure-valued delays

Related

• Local properties of solutions to non-autonomous parabolic PDEs with state-dependent delays
• Persistence in nonautonomous quasimonotone parabolic partial functional differential equations with delay
• Convergence of delay equations driven by a Hölder continuous function of order β∈(\frac13,\frac12)
• Examples of very unstable linear partial functional differential equations
• Semicycles and correlated asymptotics of oscillatory solutions to second-order delay differential equations