Well Posed

1,797
74
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?
 
21,992
3,274
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.
 
1,797
74
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.
 
21,992
3,274
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).
 
1,797
74
Sounds good!
 

Related Threads for: Well Posed

  • Last Post
Replies
2
Views
4K
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
3
Views
546
  • Last Post
Replies
3
Views
2K

Hot Threads

Top