The Analytical Solution Of Water Pollution Model With The Point Source

Water pollution incidents in China have become one of major environmentalevents. The pollutants go into the water (?)ow and it leads to the change of chem-ical, physics, biological and radioactive material in the water, which consequentlya(?)ects the e(?)ective use of water, harms human health and damages the ecologicalenvironment.Motivated by the recent event that Jilin chemical barrels leaked into the SonghuaRiver on July 28, 2010, we study a (?)rst-order stream-tributary water pollution PDEmodel with a point source and a two-dimensional reaction-di(?)usion equation withmixed boundary conditions.In the (?)rst part of this paper, we introduce some basic information. We describethe background of water pollution incidents, current research of water pollutionincidents in both China and other countries, and introduce the basic mathematicalframework/notations and reaction-di(?)usion equations in this paper.In the second part of this paper, we choose a part of river with fast (?)ow velocity,using a class of (?)rst-order transport type partial di(?)erential equation systems withthe point source to illustrate the spatial temporal change of the concentration ofthe pollutants.In the third part, adding the in(?)uence of di(?)usion, we utilize reaction-di(?)usionequations with mixed boundary conditions to build a two-dimensional water pol-lution model. We get speci(?)c forms of analytical solution by using the method ofseparation of variables.