Understanding Well-Posed Differential Equations: Tips and Techniques

[member 428835]

How to tell if a differential equation is well posed? I understand this means a solution exists and is unique. How would one determine if an ODE is well posed?

 

[micromass]

How to tell if a differential equation is well posed? I understand this means a solution exists and is unique.

I don't know. Does it? It seems to depend on author and convention.

How would one determine if an ODE is well posed?

To determine existence/uniqueness, you'll need to have a general theorem establishing them. The Picard-Lindelof theorem and the Peano existence theorem are two popular ones which show existence (and uniqueness for Picard-Lindelof) for quite some general ODE's.

 

[member 428835]

Shoot, I had a gut feeling there was some ambiguity in asking the question!

And thanks! I'll look into your suggestions! I just needed a place to start.

 

[micromass]

Do check out Ross' Differential Equations book. It's one of the best books on the topic. (Do get his large book which covers the theory, and not his small book by almost the same name which covers just the practical stuff).

 

[member 428835]

Sounds good!