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- W2005664110 abstract "This paper is concerned with the existence and stability of traveling wave solutions to first-order quasilinear hyperbolic systems. First we give explicit formulas for the n families of C 1 traveling wave solutions to homogeneous quasilinear hyperbolic system with linearly degenerate characteristic fields. Then, by means of semi-global normalized coordinates established in a neighborhood of a characteristic trajectory, we derive a new kind of formulas of wave decomposition to prove the stability of the leftmost and rightmost families of traveling wave solutions. As an application of our results, the 1-D system of the Chaplygin gas is discussed. Moreover, for the intermediate families of traveling wave solutions, their possible instability is illustrated by two examples. Dans cet article, on étudie lʼexistence et la stabilité de solutions des ondes de propagation dʼun système hyperbolique quasi-linéaire du premier ordre. On commence par donner des formules explicites pour les n familles de C 1 solutions des ondes de propagation dʼun système hyperbolique quasi-linéaire homogène avec les champs caractéristiques linéairememt dégénérés. Puis, grâce aux coordonnées normalisées établies dans un voisinage dʼune trajectoire caractéristique, on trouve un nouveau type de formules de décomposition des ondes pour dèmontrer la stabilité des familles les plus à gauche et les plus à droite des solutions des ondes de propagation. Comme exemple dʼapplication, on discute le système des gaz de Chaplygin en dimension un. Enfin, on illustre par deux exemples dʼéventuelles instabilités des familles intermédiaires des solutions des ondes de propagation." @default.
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- W2005664110 date "2013-07-01" @default.
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- W2005664110 title "Existence and stability of traveling wave solutions to first-order quasilinear hyperbolic systems" @default.
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- W2005664110 doi "https://doi.org/10.1016/j.matpur.2012.10.011" @default.
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