Question
In: Advanced Math
Find the solution to the heat equation on 0 < x < l, with u(0, t)...
Find the solution to the heat equation on 0 < x < l,
with u(0, t) = 0, ux(l, t) = 0, and u(x, 0) =
phi(x).
This is sometimes called a "mixed" boundary condition.
Solutions
Colby Messinger answered 3 years agoRelated Solutions
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
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|
Consider the backward heat equation ∂tu + uxx = 0 with u(0, x) = g(x) in...
Consider the backward heat equation ∂tu + uxx = 0 with u(0, x) =
g(x) in the periodic domain x ∈ T (Peridoc) . Use separation of
variables to solve this equation and prove that as long as g is not
a constant, the solution does not decay whent → ∞.
Heat equation: Arbitrary temperatures at ends. If the ends x = 0 and x = L...
Heat equation: Arbitrary temperatures at ends. If the ends x =
0 and x = L of the bar in the text are kept at constant
temperatures U1 and U2, respectively. The initial temp distribution
is given by u(x, 0) = f (x).
(a) What is the temperature u1(x) in the bar after a long time
(theoretically, as t → ∞)? First guess, then calculate.
(b) What is the temperature at any t. Use the heat equation
given by ut...
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
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
Consider the equation utt = uxx x ∈ (0, pi) ux(0,t) = u(pi,t) = 0 Write...
Consider the equation utt = uxx
x ∈ (0, pi)
ux(0,t) = u(pi,t) = 0
Write the series expansion for a solution u(x,t)
Consider the equation: ?̇ +2? = ?(?) with initial condition x(0) = 2 (a) If u(t)...
Consider the equation: ?̇ +2? = ?(?) with initial condition x(0)
= 2
(a) If u(t) = 0, find the solution ?(?). What is ?(?) as t ->
∞?
(b) If u(t) = 4+t, find the solution ?(?). What is ?(?) as t
-> ∞?
(c) If u(t) = ?3?, find the solution ?(?). What is
?(?) as t -> ∞?
(d) If u(t) = δ(t), find the solution ?(?). What is ?(?) as t
-> ∞?
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
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 solution to the heat equation in 3 dimensions on the half space z>0, with...
Find the solution to the heat equation in 3 dimensions on the
half space z>0, with homogeneous Neumann boundary conditions at
z=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.
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