On a nonlinear parabolic system-modeling chemical reactions in rivers
We study the global existence and qualitative properties of the solutions of nonlinear parabolic systems. Such systems commonly arise in situations pertaining to reactive transport. Particular examples include the modeling of chemical reactions in rivers or in blood streams. In this paper, we first establish a maximum principle that generates a-priori bounds for solutions to a broad class of parabolic systems. Afterward, we develop an alternative technique for establishing global bounds on solutions to a specific system of three equations that belong to a different class of parabolic systems. Finally, we prove that the only bounded traveling wave solutions to this system are constants.
Heat kernel, Maximum principle, Parabolic PDE, Reaction-diffusion systems
Chen, Wenxiong, Congming Li, and Eric S. Wright. "On a nonlinear parabolic system-modeling chemical reactions in rivers." Communications on Pure & Applied Analysis 4, no. 4 (2005): 889.
Communications on Pure and Applied Analysis