Well-posedness of Smoluchowski's coagulation equation for a class of homogeneous kernels |
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Authors: | Nicolas Fournier Philippe Laurençot |
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Institution: | a Institut Elie Cartan - Nancy, Université Henri Poincaré - Nancy I, BP 239, F-54506 Vandœuvre-lès-Nancy cedex, France b Mathématiques pour l’Industrie et la Physique, CNRS UMR 5640, Université Paul Sabatier - Toulouse 3, 118 route de Narbonne, F-31062 Toulouse cedex 4, France |
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Abstract: | The uniqueness and existence of measure-valued solutions to Smoluchowski's coagulation equation are considered for a class of homogeneous kernels. Denoting by λ∈(-∞,2]?{0} the degree of homogeneity of the coagulation kernel a, measure-valued solutions are shown to be unique under the sole assumption that the moment of order λ of the initial datum is finite. A similar result was already available for the kernels a(x,y)=2, x+y and xy, and is extended here to a much wider class of kernels by a different approach. The uniqueness result presented herein also seems to improve previous results for several explicit kernels. Furthermore, a comparison principle and a contraction property are obtained for the constant kernel. |
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Keywords: | 45K05 |
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