کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4609578 | 1338518 | 2016 | 31 صفحه PDF | دانلود رایگان |
In this paper, the smoothness properties of semiflows on C1C1-solution submanifold of a parabolic partial differential equations with state-dependent delay are investigated. The problem is formulated as an abstract ordinary retarded functional differential equation of the form du(t)/dt=Au(t)+F(ut)du(t)/dt=Au(t)+F(ut) with a continuously differentiable map G from an open subset U of the space C1([−h,0],L2(Ω)), where A is the infinitesimal generator of a compact C0C0-semigroup. The present study is continuation of a previous work [14] that highlights the classical solutions and C1C1-smoothness of solution manifold. Here, we further prove the continuous differentiability of the semiflow. We finally verify all hypotheses by a biological example which describes a stage structured diffusive model where the delay, which is the time taken from birth to maturity, is assumed as a function of a immature species population.
Journal: Journal of Differential Equations - Volume 260, Issue 7, 5 April 2016, Pages 6201–6231