Suppose u(t,x)solves the initial value problem Utt = 4Uxx + sin(wt) cos(x), u(0,x)= 0 , Ut(0,x)...

Suppose u(t,x)solves the initial value problem Utt = 4Uxx + sin(wt) cos(x),

u(0,x)= 0 , Ut(0,x) = 0. Is h(t) = u(t,0) a periodic function?

(PDE)

Expert Solution

Colby Messinger answered 2 years ago

Solve the initial value problem Utt = c^2Uxx, u(0,x)= e^-x^2 , Ut(0,x) = sin x (PDE)

Solve the Boundary Value Problem, PDE: Utt-a2uxx=0, 0≤x≤1, 0≤t<∞ BCs: u(0,t)=0 u(1,t)=cos(t) u(x,0)=0 ut(x,0)=0

Find the unique solution u of the parabolic boundary value problem Ut −Uxx =e^(−t)*sin(3x), 0<x<π, t>0,...

Find the unique solution u of the parabolic boundary value problem Ut −Uxx =e^(−t)*sin(3x), 0<x<π, t>0, U(0,t) = U(π,t) = 0, t > 0, U(x, 0) = e^(π), 0 ≤ x ≤ π.

Solve the following initial value problems: a) ut+xux= -tu, x is in R, t>0; u(x,0) =f(x),...

Solve the following initial value problems: a) ut+xux= -tu, x is in R, t>0; u(x,0) =f(x), x is in R. c) ut+ux=-tu, x is in R, t>0; u(x,0)=f(x), x is in R d)2ut+ux = -2u, x,t in R, t>0; u(x,t)=f(x,t) on the straight line x = t, where f is a given function.

Solve the following initial value problem ut + 2ux − 2u = e t+2x , u(x,...

Solve the following initial value problem ut + 2ux − 2u = e t+2x , u(x, 0) = 0

Please solve the following: ut=uxx, 0<x<1, t>0 u(0,t)=0, u(1,t)=A, t>0 u(x,0)=cosx, 0<x<1

If u(t) = < sin(8t), cos(4t), t > and v(t) = < t, cos(4t), sin(8t) >,...

If u(t) = < sin(8t), cos(4t), t > and v(t) = < t, cos(4t), sin(8t) >, use the formula below to find the given derivative. d/(dt)[u(t)* v(t)] = u'(t)* v(t) + u(t)* v'(t) d/(dt)[u(t) x v(t)] = <.______ , _________ , _______>

If u(t) = < sin(5t), cos(5t), t > and v(t) = < t, cos(5t), sin(5t) >,...

If u(t) = < sin(5t), cos(5t), t > and v(t) = < t, cos(5t), sin(5t) >, use the formula below to find the given derivative. d/dt[ u(t) * v(t)] = u'(t) * v(t) + u(t)* v'(t) d/dt [ u(t) x v(t)] = ?

Solve the nonhomogeneous heat equation: ut-kuxx=sinx, 0<x<pi, t>0 u(0,t)=u(pi,t)=0, t>0 u(x,0)=0, 0<x<pi

7. Find the solution of the following PDEs: ut−16uxx =0 u(0,t) = u(2π,t) = 0 u(x,...

7. Find the solution of the following PDEs: ut−16uxx =0 u(0,t) = u(2π,t) = 0 u(x, 0) = π/2 − |x − π/2|

Question