Asymptotic stability for an integrodifferential reaction-diffusion system

The global existence of solutions and asymptotic stability of a reaction-diffusion system

This paper studies the solutions of a reaction–diffusion system with nonlinearities that generalise the Lengyel–Epstein and FitzHugh–Nagumo nonlinearities. Sufficient conditions are derived for the global asymptotic stability of the system’s solutions and confirmed through numerical Examples.

Asymptotic Properties via an Integrodifferential Inequality

Uniform boundedness, ultimate boundedness, uniform stability, and asymptotic stability are studied by analyzing a Liapunov function satisfying v′(t) ≤ −αv(t) + √ v(t) ∫ t # ω(t, s) √ v(s)ds, t ≥ t0 ≥ 0, (# = 0 or −∞). The results are then applied to integrodifferential equations x′(t) = A(t) [ x(t) + ∫ t # F (t, s)x(s)ds ] , t ≥ t0 ≥ 0, (# = 0 or −∞), in real Hilbert space with unbounded linear...

Stability Analysis of θ-Methods for Neutral Multidelay Integrodifferential System

Asymptotic stability of constant steady states for a 2×2 reaction-diffusion system arising in cancer modelling

Dependence of tumor on essential nutrients is known to be crucial for its evolution and became one of the targets for medical therapies. Based on this fact a reaction–diffusion system with chemotaxis term and nutrient–based growth of tumors is presented. The formulation of the model considers also an influence of tumor and pharmacological factors on nutrient concentration. In the paper converge...

New Stability Criteria for Reaction-diffusion

A new variational approach to irreversible thermodynamics has been developed leading to lagrangian equations of evolution. The essential results have been presented recently in the form of a short monograph [l]. Its foundation rests on a fundamental principle of virtual dissipation. Our purpose here is to derive new stability criteria for a steady state evolution based on lagrangian equations i...