# Problem 6 [30 points Use Fourier transform to solve the heat equation U = Ura -o0<x<...

Problem 6 [30 points Use Fourier transform to solve the heat equation U = Ura -o0<x< t> 0 subject to the initial condition -1, 1 u(x,0) = -1 < x < 0 0 < x <1 x € (-00, -1) U (1,00)

This Homework Help Question: "Problem 6 [30 points Use Fourier transform to solve the heat equation U = Ura -o0<x<..." No answers yet.

We need 10 more requests to produce the answer to this homework help question. Share with your friends to get the answer faster!

0 /10 have requested the answer to this homework help question.

Once 10 people have made a request, the answer to this question will be available in 1-2 days.
All students who have requested the answer will be notified once they are available.

#### Earn Coin

Coins can be redeemed for fabulous gifts.

Similar Homework Help Questions
• ### 1. Use the Fourier Transform to solve the following problem with W1 21 (a) Find the Fourier Trans...

1. Use the Fourier Transform to solve the following problem with W1 21 (a) Find the Fourier Transform of u by applying F to the equation and initial condition; denote this function U(w, t). (b) Find u u(z, t) by taking the inverse transform of the U(w, t) you found in part (a). 1. Use the Fourier Transform to solve the following problem with W1 21 (a) Find the Fourier Transform of u by applying F to the equation and...

• ### 3. Use Fourier Transforms to solve u(0, )sin(ar) -o0 o0, t > 0, 3. Use Fourier Transforms to solve u(0, )sin(ar...

3. Use Fourier Transforms to solve u(0, )sin(ar) -o0 o0, t > 0, 3. Use Fourier Transforms to solve u(0, )sin(ar) -o0 o0, t > 0,

• ### Use Fourier Transform to solve Laplaces Equation

Really need help on this one:Use Fourier Transform to solve Laplaces Equation:uxx + uyy = 0, 0 < x < 8, -8 < y < 8,subject to:u(0, y) = g(y)

• ### Problem 1: We are interested in solving a modified form of diffusion equation given below using Fourier transforms au(x,t) The domain of the problem is-oo < x < oo and is 0 < t < oo . At...

Problem 1: We are interested in solving a modified form of diffusion equation given below using Fourier transforms au(x,t) The domain of the problem is-oo < x < oo and is 0 < t < oo . At time t = 0, the initial condition is given by u (x,0)-0 a) Take the Fourier transform on x and show that the above PDE can be transformed into the following ODE where G() is the Fourier transform of g(x) and U(w,...

• ### (4 points) Use the Fourier integral transformations to solve the heat equation д2u du 0 <...

(4 points) Use the Fourier integral transformations to solve the heat equation д2u du 0 < x u(x, 0) = 0, 100, a(0,t) (Please use "alpha" for the variable α.) n(x, t) = Jo

• ### (4 points) Use the Fourier integral transformations to solve the heat equation д2u du 0 < x u(x, 0) = 0, 100, a(0,t) (Please use "alpha" for the variable α.) n(x, t) = Jo (4 points) U...

(4 points) Use the Fourier integral transformations to solve the heat equation д2u du 0 < x u(x, 0) = 0, 100, a(0,t) (Please use "alpha" for the variable α.) n(x, t) = Jo (4 points) Use the Fourier integral transformations to solve the heat equation д2u du 0

• ### [points=4] Q4. Solve the heat equation subject to the given conditions: д?u ди О<x<п, to дх?...

[points=4] Q4. Solve the heat equation subject to the given conditions: д?u ди О<x<п, to дх? at' ди ди - (0,t) = 0, - (п,t) = 0, t>0 дх дх u(x,0) = п-х Paragraph В І := =

• ### 6. Solve the heat equation (5.17) with initial condition u(x, 0) = H(x)e-x. Write the solution...

6. Solve the heat equation (5.17) with initial condition u(x, 0) = H(x)e-x. Write the solution of the Cauchy problem for the heat equation u = kuyx - < x <®, t> 0, (5.17) with initial condition u(t,0) = {(H(x + 1) - H (1 - x)) in terms of the error function Erf () = * e ** dy.

• ### Using Fourier transform, prove that a solution of the Laplace equation in the half plane: Urn+...

Using Fourier transform, prove that a solution of the Laplace equation in the half plane: Urn+ Uyy=0,- << ,y>0, with the boundary conditions u(1,0) = f(t), - <I< u(x,y) +0,31 +0,+0, is given by r(2, y) == Love you > 0. Hint: 1. Take Fourier transform on the variable r, 2. Observe U(k, y) +0 as y → 00, 3. Use pt {e-Mliv = Vice in

• ### — дt ! [points=4] Q4. Solve the heat equation subject to the given conditions: д?u ди...

— дt ! [points=4] Q4. Solve the heat equation subject to the given conditions: д?u ди 0<х «п, t> о дх2 ди ди - (0,t) = 0, - (п,t) = 0, t>0 дх дх и(x,0) = п - 3x

Free Homework App