Abstract
Time dependent linear kinetic equations arise in a number of diverse applications in biology, chemistry and physics, as well as in various other modeling problems. Due to a tradition deeply rooted in classical mathematical physics and reinforced by the successes of quantum mechanics, such time dependent problems were initially attacked using the eigenfunction method. Yet, this method met with a relative lack of success, due to the nonnormal nature of the operators occurring in these kinetic problems, and it was supplanted by the semigroup approach, which for decades became the dominant method of time dependent kinetic theory. Despite its virtues, the semigroup approach is somewhat indirect, and is not naturally suited for treating linear evolution problems with time dependent operators, phase spaces and boundary conditions. This chapter will be devoted to an approach to these problems based on the method of characteristics.KeywordsVector FieldBorel MeasureIntegral CurveBorel FunctionIntegral CurfThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Published Version
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