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Quasi-linear Equations

  • Marin MarinEmail author
  • Andreas Öchsner
Chapter
  • 538 Downloads

Abstract

Let \(\Omega \) be a bounded domain in the \(n-\)dimensional Euclidean space \(\mathrm{I}\!\mathrm{R}^n\). The general form of a partial differential equation is: \(F(x,u, u_{x_1},\ldots ,u_{x_n}, u_{x_1x_2},\ldots , u_{x_ix_j}, u_{x_1x_2\ldots x_i},\ldots , u_{x_1x_2\ldots x_n})=0,\) where by \(u_{x_i},u_{x_ix_j}, u_{x_ix_jx_k},\ldots ,\) we have denoted partial derivatives \(\frac{\partial u}{\partial x_i}, \frac{\partial ^2 u}{\partial x_i\partial x_j}, \frac{\partial ^3 u}{\partial x_i\partial x_j\partial x_k},\ldots \).

Keywords

Quasi-linear Equations Quasi-linear Partial Differential Equations Prime Integrals Real Distinguishing Feature Real Characteristic Curves 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceTransilvania University of BrasovBrasovRomania
  2. 2.Faculty of Mechanical EngineeringEsslingen University of Applied SciencesEsslingen am NeckarGermany

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