ISSN:
1436-5081
Keywords:
Key words: Conservation laws
;
Cauchy problems
;
nonlinear geometric optics
;
generalized solutions
;
1991 Mathematics Subject Classification: 35L65
;
35L45
;
35B05
;
46F10
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. This paper is devoted to the study of Cauchy problems for regularized conservation laws in Colombeau algebras of generalized functions. The existence and uniqueness of generalized solutions to these Cauchy problems are obtained. Further, we develop a generalized variant of nonlinear geometric optics for the regularized problems. Consistency with the classical results is shown to hold for scalar conservation laws with bounded variation initial data in one space variable.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s006050050022
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