Talk:Partial differential equation: Difference between revisions
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Rewrite needed
Can somebody who understands this article rewrite the following please? "Partial differential equations also occupy a large sector of pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such as existence, uniqueness, regularity, and stability." As is, it is incomprehensible. Perhaps break it into two or three sentences? — Preceding unsigned comment added by 2600:1702:170:3B90:252F:91F:542:7612 (talk) 17:59, 26 October 2022 (UTC)
Notation and examples
Heat equation
In the section Heat equation,
the constant k is usually referred to as
thermal diffusivity.
Tianran Chen 03:56, 2004 Mar 1 (UTC)
Tianran, are you still alive? — Preceding unsigned comment added by 37.232.69.137 (talk) 04:17, 19 April 2022 (UTC)
Conceptual Definition
Arnold defines an ODE in his book as a system evolving in time having the following properties: (1) determinancy (2) finite dimensionality (3) smoothness
where by determinancy he means that the initial data of the problem completely specifies the future and the past of the system. By a finite dim. system he means one whose phase space can be localy parametrized by finite many real numbers. The smoothness property means that the system has a smooth phase space (ie. the phase space is a differentiable manifold, eg. The plane, the real line) and smooth evolution function.
What i would like to know is if there exists such a nice conceptual definition of a PDE.
Needs rewriting
The sentence:
"This solution approaches infinity if nx is not an integer multiple of π for any non-zero value of y. "
neglects to state that the solution approaches infinity as what approaches what. Mathematical functions can approach infinity as certain values of their arguments approach certain limiting values. What the limiting value(s) are is unfortunately left unstated here.
It is very important in an encyclopedia article to avoid assuming that the reader is telepathic.50.205.142.50 (talk) 13:37, 27 March 2020 (UTC)
Definition of the quasi-linear equations
I saw that in the article Method of characteristics is mentioned a quasi-linear type of equation. But the definition can't be found on Wikipedia and there's a link to wolfram Mathematica language specification. I think this article could be suited for the definition of such equations. What do you think about it? Where should it be written?
Diagramlemma (talk) 15:10, 19 June 2020 (UTC)
- If someone decides to add the definition, I have a book that can be used as a reference. MaxwellMolecule (talk) 19:13, 19 June 2020 (UTC)
- I have made this addition, see semilinear and quasilinear in the page Nick Mulgan (talk) 04:25, 27 November 2020 (UTC)