Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Well Posed

  1. Oct 23, 2015 #1

    joshmccraney

    User Avatar
    Gold Member

    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?
     
  2. jcsd
  3. Oct 23, 2015 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

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

    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.
     
  4. Oct 23, 2015 #3

    joshmccraney

    User Avatar
    Gold Member

    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.
     
  5. Oct 23, 2015 #4

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    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).
     
  6. Oct 23, 2015 #5

    joshmccraney

    User Avatar
    Gold Member

    Sounds good!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Well Posed
Loading...