Riemann Problem for a $2 \times 2$ Hyperbolic System with Linear Damping

cruz, Richard De la

doi:10.1007/s10440-020-00350-w

Cited by 12 publications

(3 citation statements)

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“…This elementary wave solution depends upon the category of characteristic fields, that is, genuinely nonlinear characteristic field involves either shock wave or rarefaction wave and at the same time linearly degenerate characteristic field involves contact discontinuity. Many researchers obtained elementary wave solution to the Riemann problem corresponding to a variety of mathematical models 3–10 . Sahoo et al 11,12 obtained exact solutions to shallow water equations and rate‐type material for the generalized Riemann problem.…”

Section: Introductionmentioning

confidence: 99%

“…Many researchers obtained elementary wave solution to the Riemann problem corresponding to a variety of mathematical models. [3][4][5][6][7][8][9][10] Sahoo et al 11,12 obtained exact solutions to shallow water equations and rate-type material for the generalized Riemann problem. Shen et al [13][14][15][16] obtained Riemann solutions for various physical models such as chemotaxis model with flux perturbation, pressure-gradient system, scaled LeRoux system, and inviscid Burgers equation.…”

Section: Introductionmentioning

confidence: 99%

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Wave interactions in pressureless Cargo–LeRoux model with flux perturbation

Sahoo

Sekhar

2023

Math Methods in App Sciences

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In this article, we discuss the wave interactions in pressureless Cargo-LeRoux model with flux perturbation. The corresponding Riemann solution in terms of a one-parameter family of curves is presented. We prove the existence and uniqueness of the solution to the Riemann problem and construct estimates for the components of the solution. Relevant amplitudes are determined while presenting the interactions of weak discontinuity with contact discontinuity and shock waves. Further, we discuss the interaction of weak shocks in detail. Finally, some test cases are treated to understand the effect of initial data and strength of the shock on the transmitted, reflected amplitudes, and jump in the acceleration of the shock.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Wave interactions in pressureless Cargo–LeRoux model with flux perturbation

Sahoo

Sekhar

2023

Math Methods in App Sciences

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“…Solving Riemann problems for systems is a fundamental topic in conservation laws. Recent work concerned with Riemann problem for non-strictly hyperbolic system has been conducted by LeFloch and De la Cruz among others [2,5].…”

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confidence: 99%

Riemann problem for a non-strictly hyperbolic system in chemotaxis

Li¹,

Mathur²

2022

DCDS-B

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The Riemann problem is solved for a system arising in chemotaxis. The system is of mixed-type and transitions from a hyperbolic to an elliptic region. It is genuinely nonlinear in the u-v plane except on the v-axis, where it is linearly degenerate. We have solved the Riemann problem in the physically relevant region up to the boundary of the hyperbolic-elliptic region, which is non-strictly hyperbolic. We also solved the problem on the linearly degenerate region. While solving the Riemann problem, we found classical shock and rarefaction waves in the hyperbolic region and contact discontinuities in the linearly degenerate region.

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