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Chapter 2 / S2.2P Problem 2 (6)
« on: January 20, 2020, 09:44:47 AM »
I have 2 questions regarding the problem.
First and foremost, after solving the characteristics, I am getting u as a function of u. I know there is a way to deal with it via the use of Inverse Function theorem (?), but I am not sure how it's done.
I have arrived at:
First, am I getting the correct equation?
Second, how do I proceed from here?
I was also wondering what's the general rule of dealing with the IVP for 3 and higher dimensional equations? After plugging in t=0, or whatever the Cauchy problem condition is, I am getting f in terms of x and y and no straight-forward way of plugging t back in.
Matter-of-factly, my question isn't specific to equation (6).
Thanks in advance; I understand if I've made the question in any way unclear.
First and foremost, after solving the characteristics, I am getting u as a function of u. I know there is a way to deal with it via the use of Inverse Function theorem (?), but I am not sure how it's done.
I have arrived at:
u=xt-f(3(t-x-y) + xy + 2u)
First, am I getting the correct equation?
Second, how do I proceed from here?
I was also wondering what's the general rule of dealing with the IVP for 3 and higher dimensional equations? After plugging in t=0, or whatever the Cauchy problem condition is, I am getting f in terms of x and y and no straight-forward way of plugging t back in.
Matter-of-factly, my question isn't specific to equation (6).
Thanks in advance; I understand if I've made the question in any way unclear.