Question

3. Solve the Neumann problem for diffusion on the half-line: ut − kuxx = 0 subject...

3. Solve the Neumann problem for diffusion on the half-line: ut − kuxx = 0 subject to u(x, 0) = φ(x), x > 0, ux(0, t) = 0, t > 0. Use an appropriate extension of the initial data to the whole real line and simplify the expression for u(x, t) so that the domain of the integral is [0, ∞). (See the notes for a similar formula for the Dirichlet problem.)

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Find the solution formula for the heat equation ut = c2 uxx on the half-infinite bar...
Find the solution formula for the heat equation ut = c2 uxx on the half-infinite bar (0 ≤ x < ∞) with Dirichlet boundary condition u(0, t) = a, for some constant a, and initial condition u(x, 0) = f(x) using the Fourier sine transform.
Solve the below boundary value equation 1. Ut=2uxx o<x<pi 0<t 2. u(0,t) = ux(pi,t) 0<t 3....
Solve the below boundary value equation 1. Ut=2uxx o<x<pi 0<t 2. u(0,t) = ux(pi,t) 0<t 3. u(x,0) = 1-2x 0<x<pi
Using separation of variables to solve the heat equation, ut = kuxx on the interval 0...
Using separation of variables to solve the heat equation, ut = kuxx on the interval 0 < x < 1 with boundary conditions ux (0, t ) = 0 and ux (1, t ) = 0, yields the general solution, ∞ u(x,t) = A0 + ?Ane−kλnt cos?nπx? (with λn = n2π2) n=1DeterminethecoefficientsAn(n=0,1,2,...)whenu(x,0)=f(x)= 0, 1/2≤x<1 .
1. Solve fully the heat equation problem: ut = 5uxx u(0, t) = u(1, t) =...
1. Solve fully the heat equation problem: ut = 5uxx u(0, t) = u(1, t) = 0 u(x, 0) = x − x ^3 (Provide all the details of separation of variables as well as the needed Fourier expansions.)
Solve ut=uxx, 0 < x < 3, given the following initial and boundary conditions: - u(0,t)...
Solve ut=uxx, 0 < x < 3, given the following initial and boundary conditions: - u(0,t) = u(3,t) = 1 - u(x,0) = 0 Please write clearly and explain your reasoning.
On this problem, be sure to discuss the dynamic behavior and characteristics of the graphs. 3...
On this problem, be sure to discuss the dynamic behavior and characteristics of the graphs. 3 (a) Solve AND find the characteristics curve for the eqtn :  ut + (x-t)ux = 0. (b) Find the solution to the initial value problem u(0, x) = e^{-x^2}, (c) and discuss its dynamic behavior.
4. a) solve the ff: Initial Value Problem: Eqtn : 2ut + XUx =0 U(X,0) =...
4. a) solve the ff: Initial Value Problem: Eqtn : 2ut + XUx =0 U(X,0) = f(X) b) Assuming f is C1,verify that u(x,t) =   f (xe^ -t/2 ) is a solution. 5) a) Solve the Initial Value problem: Eqtn : 2ut + XUx =0   U(X,0) = -X^2 +2X, ON THE DOMAIN 0 < x< 2 , t>2 b ) DRAW THE GRAPHS OF THE SOL. U(X,ti) as a function of X, FOR ti= 0, 0.1, 0.5, 1.0 c) HOW DO...
Solve the following initial/boundary value problem: ∂u(t,x)/∂t = ∂^2u(t,x)/∂x^2 for t>0, 0<x<π, u(t,0)=u(t,π)=0 for t>0, u(0,x)=sin^2x...
Solve the following initial/boundary value problem: ∂u(t,x)/∂t = ∂^2u(t,x)/∂x^2 for t>0, 0<x<π, u(t,0)=u(t,π)=0 for t>0, u(0,x)=sin^2x for 0≤x≤ π. if you like, you can use/cite the solution of Fourier sine series of sin^2(x) on [0,pi] = 1/4-(1/4)cos(2x) please show all steps and work clearly so I can follow your logic and learn to solve similar ones myself.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT