An explicit solution of Burgers equation with stationary point source

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Existence, uniqueness and regularity of the global weak solution to the Burgers equation with a reaction term is shown when the reaction term is given as a time independent point source and produces heat constantly. An explicit solution is obtained and used to show the long time asymptotic convergence of the solution to a steady state. For the heat equation case without any convection the solution diverges everywhere as time increases and hence it is the first order convection term that gives the compactness of the solution trajectory of the Burgers equation with reaction.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2014-10
Language
English
Article Type
Article
Keywords

DIFFUSION-CONVECTION EQUATION; ASYMPTOTIC-BEHAVIOR; POSITIVE SOLUTIONS; SPACE

Citation

JOURNAL OF DIFFERENTIAL EQUATIONS, v.257, no.7, pp.2520 - 2542

ISSN
0022-0396
DOI
10.1016/j.jde.2014.05.046
URI
http://hdl.handle.net/10203/190123
Appears in Collection
MA-Journal Papers(저널논문)
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