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

A. Nastase ()
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A. Nastase: Aachen University, RWTH

A chapter in Integral Methods in Science and Engineering, 2011, pp 253-260 from Springer

Abstract: 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: $$\sum\limits^{M}_{i=1}\left[ \sum\limits^{M}_{j=1} a_{ij}x_{i}x_{j} + 2a_{i,M+1}x_{i} \right]+ a_{M+1,M+1}= 0.$$

Date: 2011
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DOI: 10.1007/978-0-8176-8238-5_24

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