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- Title
Initial boundary value problems for some damped nonlinear conservation laws.
- Authors
Yadav, Manoj K.
- Abstract
In this paper, we study the non-negative solutions of initial boundary value problems for some damped nonlinear conservation laws on the half line modelled by first order nonlinear hyperbolic PDEs. We consider the class of initial profile which are non-negative, bounded and compactly supported. Using the method of characteristics and Rankine-Hugoniot jump condition, an entropy solution is constructed subject to a top-hat initial profile. Then the large time behaviour of the constructed entropy solution is obtained. Finally, taking recourse to some comparison principles and the method of super and sub solutions the large time behaviour of entropy solutions subject to the general class of bounded and compactly supported initial profiles are established as the large time behaviour of the entropy solution subject to top-hat initial profiles.
- Subjects
BOUNDARY value problems; CONSERVATION laws (Mathematics); NONNEGATIVE matrices; RANKINE cycle; ENTROPY; RIEMANN-Hilbert problems
- Publication
Electronic Journal of Qualitative Theory of Differential Equations, 2015, Issue 84-100, p1
- ISSN
1417-3875
- Publication type
Article
- DOI
10.14232/ejqtde.2015.1.86