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Asymptotic behaviour of traveling waves for the delayed FisherKPP equation,
 J. Differential Equations
, 2014
"... Abstract In this work we study the behaviour of travelling wave solutions for the diffusive Hutchinson equation with time delay. Using a phase plane analysis we prove the existence of travelling wave solution for each wave speed c ≥ 2. We show that for each given and admissible wave speed, such tra ..."
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Abstract In this work we study the behaviour of travelling wave solutions for the diffusive Hutchinson equation with time delay. Using a phase plane analysis we prove the existence of travelling wave solution for each wave speed c ≥ 2. We show that for each given and admissible wave speed, such travelling wave solutions converge to a unique maximal wavetrain. As a consequence the existence of a nontrivial maximal wavetrain is equivalent to the existence of travelling wave solution nonconverging to the stationary state u = 1.
ON THE FUNDAMENTAL SOLUTION OF LINEAR DELAY DIFFERENTIAL EQUATIONS WITH MULTIPLE DELAYS
"... Abstract. For a class of linear autonomous delay differential equations with parameter α we give upper bounds for the integral ´ ∞ 0 X (t, α)  dt of the fundamental solution X (·, α). The asymptotic estimations are sharp at a critical value α0 where x = 0 loses stability. We use these results to s ..."
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Abstract. For a class of linear autonomous delay differential equations with parameter α we give upper bounds for the integral ´ ∞ 0 X (t, α)  dt of the fundamental solution X (·, α). The asymptotic estimations are sharp at a critical value α0 where x = 0 loses stability. We use these results to study the stability properties of perturbed equations. Key words and phrases: linear delay differential equation, fundamental solution, Laplace transform, discrete Lyapunov functional 2000 Mathematics Subject Classification: 34K06, 34K20 1.