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A nonlocal coagulation-fragmentation model

Mirosław Lachowicz, Dariusz Wrzosek (2000)

Applicationes Mathematicae

A new nonlocal discrete model of cluster coagulation and fragmentation is proposed. In the model the spatial structure of the processes is taken into account: the clusters may coalesce at a distance between their centers and may diffuse in the physical space Ω. The model is expressed in terms of an infinite system of integro-differential bilinear equations. We prove that some results known in the spatially homogeneous case can be extended to the nonlocal model. In contrast to the corresponding local...

Abstract theory of variational inequalities with Lagrange multipliers and application to nonlinear PDEs

Takeshi Fukao, Nobuyuki Kenmochi (2014)

Mathematica Bohemica

Recently, we established some generalizations of the theory of Lagrange multipliers arising from nonlinear programming in Banach spaces, which enable us to treat not only elliptic problems but also parabolic problems in the same generalized framework. The main objective of the present paper is to discuss a typical time-dependent double obstacle problem as a new application of the above mentioned generalization. Actually, we describe it as a usual parabolic variational inequality and then characterize...

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