Split delta shocks and applications to conservation law systems

Abstract

There are many real models in which unbounded solution to conservation law system occur. Most often we have some kind of delta function in the solution as a result of the accumulation of mass or some other variable. There is no general method of approaching such problems with nonlinearities. This dissertation provides solutions to conservation law systems that contain division by a dependent variable, which is a problematic part when working with measures. For example, a basic model of chromatography and similar chemical processes has a division with a variable that is unbounded in some cases. The denition of the split delta shock and the general method of using it in such systems is given. Finally, the solution for the singular chromatography model is given.

Postoji mnogo realnih modela u kojima se javljaju neoranicena resenja zakona odrzanja. Najcesce imamo neku vrstu delta funkcije u resenju kao posledicu nagomilavanja mase ili neke druge velicine. Ne postoji opsti metod prilaza takvim problemima sa nelinearnostima. U ovoj disertaciji su data resenja problema zakona odrzanja koja sadrze delenje zavisnom promenljivom, sto je problematican deo kod rada sa merama. Na primer, osnovni model hromatograje i slicnih hemijskih procesa ima delenje promenljivom koja je neogranicena u nekim slucajevima. Data je denicija inverza delenjog delta udarnog talasa i opsti metod primene u takvim sistemima. Na kraju je dato resenje kod modela singularne hromatograje.