10.1186/2251-7456-6-47

An analysis on classifications of hyperbolic and elliptic PDEs

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  • Hassan Eltayeb1,
  • Adem Kılıçman*2,
  • Ravi P Agarwal3,
  1. Mathematics Department, College of Science, King Saud University, Riyadh, 11451, SA
  2. Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia, UPM, Serdang, Selangor, 43400, MY
  3. Department of Mathematics, Texas A&M University - Kingsville, Kingsville, TX, 78363-8202, US

Published in Issue 2012-10-09

How to Cite

Eltayeb, H., Kılıçman, A., & Agarwal, R. P. (2012). An analysis on classifications of hyperbolic and elliptic PDEs. Mathematical Sciences, 6(1). https://doi.org/10.1186/2251-7456-6-47
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Abstract

Abstract Purpose Our aim in this study is to generate some partial differential equations (PDEs) with variable coefficients by using the PDEs with non-constant coefficients. Methods Then by applying the single and double convolution products, we produce some new equations having polynomials coefficients. We then classify the new equations on using the classification method for the second order linear partial differential equations. Results Classification is invariant under single and double convolutions by applying some conditions, that is, we identify some conditions where a hyperbolic equation will be hyperbolic again after single and double convolutions. Conclusions It is shown that the classifications of the new PDEs are related to the coefficients of polynomials which are considered during the process of convolution product.

Keywords

  • Hyperbolic equation,
  • Elliptic equation,
  • Single and double convolution,
  • Classification of PDE,
  • 35L05; 44A35
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References

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