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2005, Volume 4, Issue 4: 889-899. Doi: 10.3934/cpaa.2005.4.889
This issue Previous Article Structure of positive radial solutions including singular solutions to Matukuma's equation Next Article

On a nonlinear parabolic system-modeling chemical reactions in rivers

  • 1.

    Department of Mathematics, Southwest Missouri State University, Springfield, MO 65804

  • 2.

    Department of Applied Mathematics, University of Colorado at Boulder

  • 3.

    Department of Mathematics, University of Montana-Western, 710 S. Atlantic Street Dillon, MT 59725-3598

Received:  October 31, 2004
Revised:  April 30, 2005
Published:  November 2005
Abstract Related Papers Cited by
    Abstract
  • 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.
    Mathematics Subject Classification: Primary: 35K05, 35K45, 35K55, 35K57.

    Citation:
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