Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Consider $x'=f(x)$ such that $(x_1,x_2)\mapsto(-x_1+2x_2,-2x_1-x_2)$.

show that for two solutions $x(t)$ and $y(t)$ of the above differential equation we have:

$\lVert x(t)-y(t)\rVert \leq e^{-t}\lVert x(0)-y(0)\rVert$

Please can you show me how to apply the gronwall lemma to this.

This part that is most confusing to is how to use the lemma and how to use the lemma with $(x_1,x_2)\mapsto(-x_1+2x_2,-2x_1-x_2)$

p.s i dont understand why this has been voted down!! The guidelines for the site state that if a questions hasnt been answered or answered properly you can ask it again!

Thanks very much

share|improve this question
    
    
that wasnt an accepted answer though, plus the answer looks very different to what mine is ment to look like!! In which case you are allowed to ask the question again, that person did not get their answered properly otherwise i would be using theirs! I read the guidelines before i posted this as i had already been through all other gronwall questions and seen that one. –  sarah Mar 19 '13 at 1:31
add comment

1 Answer

I think this is how your would answer the question but not sure and dont quite get all of it either http://www.math.ucla.edu/~ralston/33b.1.10f/Gronwall.pdf

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.