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Nonlinear Wave Interactions in a Macroscopic Production Model

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Abstract

In this article, we study the exhaustive analysis of nonlinear wave interactions for a 2 × 2 homogeneous system of quasilinear hyperbolic partial differential equations (PDEs) governing the macroscopic production. We use the hodograph transformation and differential constraints technique to obtain the exact solution of governing equations. Furthermore, we study the interaction between simple waves in detail through exact solution of general initial value problem. Finally, we discuss the all possible interaction of elementary waves using the solution of Riemann problem.

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Acknowledgements

The fist author (Minhajul) is highly thankful to Ministry of Human Resource Development, Government of India, for the institute fellowship (grant no. IIT/ACAD/PGS & R/F.II/2/14MA90J08) from IIT Kharagpur. The second author (TRS) would like to thank SERB, DST, India (Ref. No. MTR/2019/001210) for its financial support through MATRICS grant. We thank Prof. N. Manganaro and Prof. C. Curro (University of Messina) for their valuable suggestions and comments.

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Authors and Affiliations

  1. Center for Applicable Mathematics, Tata Institute of Fundamental Research, Bangalore, Karnataka, 560065, India

    Minhajul

  2. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur-2, India

    Minhajul & T. Raja Sekhar

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  1. Minhajul
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  2. T. Raja Sekhar
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Correspondence to Minhajul.

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Minhajul, Raja Sekhar, T. Nonlinear Wave Interactions in a Macroscopic Production Model. Acta Math Sci 41, 764–780 (2021). https://doi.org/10.1007/s10473-021-0309-8

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  • DOI: https://doi.org/10.1007/s10473-021-0309-8

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