A Note on Shock Profiles in Dissipative Hyperbolic and Parabolic Models
Publications de l'Institut Mathématique, (N.S.) 84 (2008) no. 98.

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This note presents a comparative study of shock profiles in dissipative systems. Main assumption is that both hyperbolic and parabolic model are reducible to the same underlying equilibrium system when dissipative effects are neglected. It will be shown that the highest characteristic speed of equilibrium system determines the critical value of the shock speed for which downstream equilibrium state bifurcates. It will be also shown that it obeys the same transcritical bifurcation pattern in hyperbolic, as well as in parabolic case.
Mots-clés : Hyperbolic and parabolic balance laws, dissipative models, shock profile, stability, bifurcation 
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     author = {Srboljub S. Simi\'c},
     title = {A {Note} on {Shock} {Profiles} in {Dissipative} {Hyperbolic} and {Parabolic} {Models}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {97 - 107},
     publisher = {mathdoc},
     volume = {(N.S.) 84},
     number = {98},
     year = {2008},
     zbl = {1199.35221},
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Srboljub S. Simić. A Note on Shock Profiles in Dissipative Hyperbolic and Parabolic Models. Publications de l'Institut Mathématique, (N.S.) 84 (2008) no. 98. https://geodesic-test.mathdoc.fr/item/PIM_2008_N_S_84_98_a5/