Communications in Mathematical Sciences

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We translate a coagulation-framentation model, describing the dynamics of animal group size distributions , into a model for the population distribution and associate the nonlinear evolution equation with a Markov jump process of a type introduced in classic work of H. McKean. In particular this formalizes a model suggested by H.-S. Niwa [J. Theo. Biol. 224 (2003)] with simple coagulation and fragmentation rates. Based on the jump process, we develop a numerical scheme that allows us to approxim...

Instationary drift-diffusion problems with Gauss–Fermi statistics and field-dependent mobility for organic semiconductor devices

In this paper, an asymptotic traveling wave of a free boundary problem related to a pricing model for corporate bond with multiple credit rating migration risk is studied. The pricing model is captured by a free boundary problem, whose existence, uniqueness and regularity of the solution are obtained such that the rationality of the model is guaranteed. The existence of a unique traveling wave in the free boundary problem is established with some risk discount rate condition satisfied. The induc...

An application of FDM by Gibou to a numerical blow-up for nonlinear evolution equations on a domain \Omega \subset \mathbb{R}^N

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