TY - JOUR
T1 - Admissibility of self-similar weak solutions of systems of conservation laws in two space variables and time
AU - Sever, Michael
PY - 2009
Y1 - 2009
N2 - By means of an example, we postulate that the familiar local entropy conditions on discontinuities are far from sufficient to distinguish admissible weak solutions of systems of conservation laws in two space dimensions and time. We consider the familiar problem of the reflection of an incident shock by a wedge for the "nonlinear wave system", finding a plethora of self-similar weak solutions (or possibly approximate weak solutions) satisfying the usual entropy condition for this system. The multiplicity of such solutions arises from unneeded freedom in the algorithm for constructing solutions, and is directly related to a modest reduction in the assumed regularity of the solution in comparison to that assumed in previous work on this problem. We conclude that if the limit of vanishing viscosity indeed exists for such problems, an additional physical principle is needed to characterize admissible weak solutions.
AB - By means of an example, we postulate that the familiar local entropy conditions on discontinuities are far from sufficient to distinguish admissible weak solutions of systems of conservation laws in two space dimensions and time. We consider the familiar problem of the reflection of an incident shock by a wedge for the "nonlinear wave system", finding a plethora of self-similar weak solutions (or possibly approximate weak solutions) satisfying the usual entropy condition for this system. The multiplicity of such solutions arises from unneeded freedom in the algorithm for constructing solutions, and is directly related to a modest reduction in the assumed regularity of the solution in comparison to that assumed in previous work on this problem. We conclude that if the limit of vanishing viscosity indeed exists for such problems, an additional physical principle is needed to characterize admissible weak solutions.
UR - http://www.scopus.com/inward/record.url?scp=70350042032&partnerID=8YFLogxK
U2 - 10.1142/S0219891609001897
DO - 10.1142/S0219891609001897
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AN - SCOPUS:70350042032
SN - 0219-8916
VL - 6
SP - 433
EP - 481
JO - Journal of Hyperbolic Differential Equations
JF - Journal of Hyperbolic Differential Equations
IS - 3
ER -