Solve the heat flow problem 5 t>0,0<<7, (0,t) = 0, t>0, Od (1, t) = 0,...
əz2(7,t), 0< < 4, t > 0 3 2,0<<< v(z,t) = { (1 point) Solve the heat problem with non-homogeneous boundary conditions ди au (2,t) at u(0,t) = 0, u(4, t) = 3, t > 0, u(2,0) 2,0<2<4. Recall that we find h(2), set v2,t) = u(2,t) – h(2), solve a heat problem for v2,t) and write uz,t) = v(x, t) +(2). Find h(1) h(x) = The solution u(x, t) can be written as u(x, t)=h(2) +v(2,t), where v(x, t)...
PROBLEM 4. Determine the function u = u(t, x) if Ut = Uzz, t> 0, x € (0, 7), and u(0, x) = cos (x), uz(t, 0) = uz(t, 7) = 0.
7. (a) Find the solution of the heat conduction problem: Suxx = ut, 0<x< 5, u(0, 1) = 20, tu(5, 1) = 80, 1>0 u(x,0) = f(x) = 12x + 20 + 13sin(tor) - 5sin(3 tex). (b) Find lim u(2, t). (c) If the initial condition is, instead, u(x,0) = 10x – 20 + 13sin( Tox) - 5sin(3 7ox), will the limit in (b) be different? What would the difference be?
Solve the heat flow problem: au t> 0, ди (x, t) = 2 (x, t), 0<x< 1, ot дх2 uz(0, t) = uz(1,t) = 0, t>0, u(x,0) = 1- x, 0 < x < 1.
-). Solve the initial and boundary value problem: uUx=0, TE (0,), t > 0, U (0,t) = u(,t) = 0, >0, u(,0) - cos', 1€ (0,7).
solve a, b , c 1. Consider the heat flow problem on the real line, where u(x,t), t> 0 is the temperature at point x at time t: ди 1 t> 0 at 28.2 (u(2,0) = sin() (a) What is the thermal diffusitivity constant B? (b) Find the intervals of r where the temparature will increase at t = 0. (c) Sketch the graph of the temperature at t = 0. (d) On the same axes as in (e), sketch...
(1 point) Solve the nonhomogeneous heat problem Ut Uzz + 3 sin(3.c), 0<x<1, u(0,t) = 0, u(T,t) = 0 u(2,0) sin(52) u(x, t) = Steady State Solution lim oo u(a,t) =
Problem 8 In the given circuit i(0) = 3A Determine: a) i(t) (5 points) and b) vo(t) (5 points) for t > 0 cos(5t) A 0 3h 5 *,
8. Solve V?u=0, 2<r<4,0<O<21, (u(2,0) = sin 0, u(4,0) = cos 0,0 5 0 5 21.
(1 point) Solve the heat problem uturr-Cos (x), 0 < x < T, и, (0, t) — 0, и, (т, t) — 0 и(т, 0) — 1 и(т, t) — u(x, t) = Steady State Solution lim