, ? ) × (0, a ? ) × ?) supportés en temps dans un ensemble de Lebesgue quelconque de mesure positive dans (0, ? ). Le but est d'obtenir les résultats associés de contrôle en temps optimal et un principe de type "bang-bang, Ce chapitre reprend la méthodologie du chapitre précédent afin de démontrer le contrôle à zéro des équations de Lotka et McKendrick avec diffusion, avec des contrôles u ? L ?

. .. , Some background on the Lotka-McKendrick semigroup without diffusion105 IV.2.1 The free diffusion semigroup in L 2 (0, a ? ), p.107

. .. , 110 IV.3.1 The Lotka-McKendrick semigroup with diffusion in L 2, The population dynamics with diffusion

, IV.3.2 Stability results in L ?

, Proof of the main result

, Lack of null controllability for the Lotka-McKendrick equation with spatial diffusion and positivity constraints For almost every (a, x) ? (0, a ? ) × ?, we set p 0 (a, x) := h 0 (x)

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