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Solution of a new class of nonlinear kinetic models of population dynamics. (English) Zbl 0853.35050
This paper deals with the analysis of a new class of models of population dynamics with stochastic interaction. These models are characterized by a mathematical structure similar to the one of the models of the phenomenological kinetic theory and, in particular, of the Boltzmann equation. Indeed, the evolution equation is defined by a system of integro-differential equations with quadratic or cubic nonlinearity.
This paper deals with the qualitative analysis of models with multiple interactions. The second section deals with the modelling of the population dynamics, and the third section with the qualitative analysis of the solutions to the initial value problem and with the existence of equilibrium solutions.

MSC:
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
45K05 Integro-partial differential equations
92D25 Population dynamics (general)
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