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A gradient estimate for solutions of the heat equation. II

Charles S. Kahane — 2001

Czechoslovak Mathematical Journal

The author obtains an estimate for the spatial gradient of solutions of the heat equation, subject to a homogeneous Neumann boundary condition, in terms of the gradient of the initial data. The proof is accomplished via the maximum principle; the main assumption is that the sufficiently smooth boundary be convex.

A note on the convolution theorem for the Fourier transform

Charles S. Kahane — 2011

Czechoslovak Mathematical Journal

In this paper we characterize those bounded linear transformations T f carrying L 1 ( 1 ) into the space of bounded continuous functions on 1 , for which the convolution identity T ( f * g ) = T f · T g holds. It is shown that such a transformation is just the Fourier transform combined with an appropriate change of variable.

Population Dynamics of Grayling: Modelling Temperature and Discharge Effects

S. CharlesJ.-P. MalletH. Persat — 2010

Mathematical Modelling of Natural Phenomena

We propose a matrix population modelling approach in order to describe the dynamics of a grayling (, L. 1758) population living in the Ain river (France). We built a Leslie like model, which integrates the climate changes in terms of temperature and discharge. First, we show how temperature and discharge can be related to life history traits like survival and reproduction. Second, we show how to use the population model to precisely examine the life cycle of grayling : estimated numbers of individuals...

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