SCALING PROPERTY OF THE GLIMM FUNCTIONAL
Angela L. Rodriguez1, Jairo E. Alba2, Juan C. Juajibioy3
1 School of Mathematics and Statistics
Universidad Pedagógica y Tecnológica de Colombia
North Central Avenue 39-115,
Tunja, Boyaca, 150003, COLOMBIA
2 School of Mathematics and Statistics
Universidad Pedagógica y Tecnológica de Colombia
North Central Avenue 39-115,
Tunja, Boyaca, 150003, COLOMBIA
3 School of Mathematics and Statistics
Universidad Pedagógica y Tecnológica de Colombia
North Central Avenue 39-115,
Tunja, Boyaca, 150003, COLOMBIA

Abstract

In this paper we study a new property for the Glimm potential introduced by L. Caravenna [3]. This new property enable us to study scalar conservation laws with a particular source term called linear damping. By the operator splitting method joined with the polygonal approximation method introduced by C. Dafermos [4] we shown the well-posedness of the Cauchy problem for scalar conservation laws with linear damping and finally we show that the solution exponentially decays.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 35
Issue: 4
Year: 2022

DOI: 10.12732/ijam.v35i4.5

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