Global Boundedness for a Delay Differential Equation
Copyright policy )Global Boundedness for a Delay Differential Equation
The inequality ( ∂ t u − Δ u ) ( t , x ) ≤ u ( t , x ) ( 1 − u ( t − τ , x ) ) ({\partial _t}u - \Delta u)(t,\,x)\qquad \leq \qquad u(t,\,x)(1 - u(t - \tau ,\,x)) is investigated. It is shown that nonnegative solutions of the Dirichlet problem in a bounded interval remain bounded as time goes to infinity, whereas in a more dimensional domain, in general, this holds only if the delay is not too large.
Hutchinson's equation, diffusion, Nonlinear differential equations in abstract spaces, Asymptotic theory of functional-differential equations, Population dynamics (general), differential inequality, population dynamics, Nonlinear parabolic equations, global bands, Stability in context of PDEs
Hutchinson's equation, diffusion, Nonlinear differential equations in abstract spaces, Asymptotic theory of functional-differential equations, Population dynamics (general), differential inequality, population dynamics, Nonlinear parabolic equations, global bands, Stability in context of PDEs
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