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Asymptotic Behavior of Elliptic Quadratic Algebraic Equations with Variable Coefficients, and Aerodynamical Applications

In: Integral Methods in Science and Engineering

Author

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  • A. Nastase

    (Aachen University, RWTH)

Abstract

The quadratic partial differential equations that govern mathematical physics can be reduced to the study of equivalent quadratical algebraic equations (QAEs) with variable coefficients. The qualitative analysis of the asymptotical behaviors of the QAEs in the vicinity of their critical lines (surfaces or hypersurfaces) gives the possibility to find the critical lines (surfaces or hypersurfaces) of the PDEs of mathematical physics. Further, let us consider a QAE of elliptic or hyperbolic type: $$\sum\limits^{M}_{i=1}\left[ \sum\limits^{M}_{j=1} a_{ij}x_{i}x_{j} + 2a_{i,M+1}x_{i} \right]+ a_{M+1,M+1}= 0.$$

Suggested Citation

  • A. Nastase, 2011. "Asymptotic Behavior of Elliptic Quadratic Algebraic Equations with Variable Coefficients, and Aerodynamical Applications," Springer Books, in: Christian Constanda & Paul J. Harris (ed.), Integral Methods in Science and Engineering, edition 1, pages 253-260, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-8238-5_24
    DOI: 10.1007/978-0-8176-8238-5_24
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