Let u(x, t) be the solution in [0, 1] [0, +) of the problem 4uxx Utt...

 

Transcribed Image Text:

Let u(x, t) be the solution in [0, 1] [0, +) of the problem 4uxx Utt = a)Find f(1/3), where u|x=0= ur=1 = 0 ult=0 = 4 sin (7x), ut t=0 = 30x(1-x) f(t) = [ [u(x, t) + 4u(x, t)] dr Hint: the integral has the meaning of the energy. What happens to the energy of a closed system? What is f'(t)? Could you prove your answer and use it to solve the problem? b)Find u(x, 2) Let u(x, t) be the solution in [0, 1] [0, +) of the problem 4uxx Utt = a)Find f(1/3), where u|x=0= ur=1 = 0 ult=0 = 4 sin (7x), ut t=0 = 30x(1-x) f(t) = [ [u(x, t) + 4u(x, t)] dr Hint: the integral has the meaning of the energy. What happens to the energy of a closed system? What is f'(t)? Could you prove your answer and use it to solve the problem? b)Find u(x, 2)

Answer rating: 100% (QA)

To solve the given problem we can first find the general solution to the ... View the full answer