Understanding Non-Linear PDEs: Causes and Implications

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Discussion Overview

The discussion centers around the characteristics that define non-linear partial differential equations (PDEs) and seeks to clarify the concept of non-linearity in the context of differential equations.

Discussion Character

  • Conceptual clarification

Main Points Raised

  • One participant asks for clarification on what makes a PDE non-linear.
  • Another participant inquires about the criteria for non-linearity in ordinary differential equations.
  • A third participant questions the understanding of the term "nonlinear" itself.
  • A later reply suggests that non-linearity is characterized by the presence of a non-linear function of the dependent variable within the equation.
  • There is an implication that some participants may be surprised by the initial question regarding non-linearity in PDEs.

Areas of Agreement / Disagreement

The discussion does not reach a consensus, as participants express varying levels of understanding regarding non-linearity in differential equations.

robousy
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What makes a PDE non-linear please?

Thanks!
 
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Do you know what makes an ordinary diff. eq. non-linear?
 
Do you know what nonlinear means? :)
 
Having a non-linear function of the dependent function anywhere in the equation. I suspect arildno and Tide were wondering how you could be studying partial differential equations if you don't know what "non-linear" means!
 

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