A system of non-strictly hyperbolic conservation laws arising in elasticity theory

Keyfitz, Barbara Lee; Kranzer, Herbert C.

doi:10.1007/bf00281590

Cited by 278 publications

(130 citation statements)

References 7 publications

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“…[9],e.g.). The shock structure of spatial motions of elastic strings has recently been analyzed by [13]. Thus the smoothness assumptions made in Section 2 are completely unwarranted for elastic strings at least.…”

Section: The Equations For Large Vibrations Of Stringsmentioning

confidence: 99%

The Equations for Large Vibrations of Strings

Antman¹

1980

The American Mathematical Monthly

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Section: The Equations For Large Vibrations Of Stringsmentioning

confidence: 99%

The Equations for Large Vibrations of Strings

Antman¹

1980

The American Mathematical Monthly

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“…Note that the above system when = 0 and A = 0 was studied in [3,4]. A travelling wave with speed s = 0 to the system (2.15) satisfies the differential equations .…”

Section: Theorem 22 (A Priori Estimate) Let (U(ξ) V(ξ)) Be a Solutmentioning

confidence: 99%

Existence of strong travelling wave profiles to $2\times 2$ systems of viscous conservation laws

Yang

Zhang

Zhu

2007

Proc. Amer. Math. Soc.

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Abstract. In this paper, we prove the existence of strong travelling wave profiles for a class of 2 × 2 viscous conservation laws when the corresponding invisid systems are hyperbolic. Besides some technical assumptions, the only main assumption is the hyperbolicity. Therefore, the existence theory can be applied to systems which are not strictly hyperbolic. Moreover, the characteristic fields can be neither genuinely nonlinear nor linearly degenerate.

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“…System (1) arises as a model for the stretched elastic string to describe the propagation of forward longitudinal and transverse waves [1,2]. It is also used to illustrate certain features of the solar wind in magnetohydrodynamics [3,4].…”

Section: Introductionmentioning

confidence: 99%

The Perturbed Riemann Problem for Special Keyfitz-Kranzer System with Three Piecewise Constant States

Jiang

Shen

2017

Advances in Mathematical Physics

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The Riemann problem for a special Keyfitz-Kranzer system is investigated and then seven different Riemann solutions are constructed. When the initial data are chosen as three piecewise constant states under suitable assumptions, the global solutions to the perturbed Riemann problem are constructed explicitly by studying all occurring wave interactions in detail. Furthermore, the stabilities of solutions are obtained under the specific small perturbations of Riemann initial data.

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A system of non-strictly hyperbolic conservation laws arising in elasticity theory

Cited by 278 publications

References 7 publications

The Equations for Large Vibrations of Strings

The Equations for Large Vibrations of Strings

Existence of strong travelling wave profiles to $2\times 2$ systems of viscous conservation laws

The Perturbed Riemann Problem for Special Keyfitz-Kranzer System with Three Piecewise Constant States

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