I need this equation's analytical solution with this non-homogenous boundary conditions
I need this equation's analytical solution with this non-homogenous boundary conditions =07 , 0 x L,120...
PDE Problem: homogenous diffusion equation with non-homogenous
boundary conditions
27. Solve the nonhomogeneous initial boundary value problem | Ut = kuzz, 0 < x < 1, t > 0, u(0, t) = T1, u(1,t) = T2, t> 0, | u(x,0) = 4(x), 0 < x < 1. for the following data: (c) T1 = 100, T2 = 50, 4(x) = 1 = , k = 1. 33x, 33(1 – 2), 0 < x <a/2, /2 < x < TT, [u(x,...
3) (1 point) The boundary layer flow separates from the surface if (a) du/dy=0 and dp/dx = 0 (b) du/dy = 0 and dp/dx > 0 (c) du/dy = 0 and dp/dx < 0 (d) The boundary layer thickness is zero
4. [10] Find the solution to given initial-boundary value problem: 4uxx = ut 0<x<TI, t> 0 u(0,t) = 5, uit, t) = 10, t> 0 u(x,0) = sin 3x - sin 5x, 0<x<T
5. Given y,-t is a solution of t2y" + 2t1-2y = 0, for t > 0, find a second solution y2.
Apply separation of variables and solve the following boundary value problem 0 < x < t> 0 t>O Ytt(x, t) = 25 yxx(x, t) ya(0,t) = y2(7,t) = y(x,0) = f(x) yt(x,0) = g(x) 0 << 0 <r<a
QUESTION 2 Consmder the problem ди 2k, 0<r< 1, t>O оt and the boundary conditions u(0,t)= 1, u (1,t) = 3, t > 0 (a) Find the equiltbrium solutiou ug (r) (b) Find the solution u (z.t) of the PDE and the boundary condition which also satisfies the mitial condition (,0)-1+++sin (3wx), 0<o< 1 [25]
4. Consider the boundary value problem defined by the partial differential equation д?и д?и = 0, ду? y > 0, да? with boundary conditions u(0, y) = u(T,y) = 0, u(x, 0) = 1 and limy-v00 |u(x, y)|< 0o. (a) Use separation of variables to find the eigenvalues and general series solution in terms of the normal modes. (b) Impose the inhomogeneous boundary condition u(x,0) = 1 to find the constants in the general series solution and hence the solution...
(1 point) Suppose we have ut = aʻuzz, 0 < x <1,t > 0, boundary conditions are u(0,t) = u(1,t) = 0, and the initial condition is u(x,0) = sin(T2). What will be the behavior of u(x, t) as time increases. There may be more than one correct answer. You do not need to solve the equation to answer this question. A. The solution behaves unpredictably. B. The solution increases to infinity. OC. For a fixed t, the solution will...
Let u be the solution to the initial boundary value problem for the Heat Equation, фа(t, x)-5 &n(t, x), t E (0,00), x E (0, 1); with initial condition 2 r-, 1 and with boundary condition:s n(t, 0)=0, rn(t, 1-0. Find the solution u using the expansion with the normalization conditions vn (0)-1, wn a. (3/10) Find the functions wz, with indexn> 1 b. (3/10) Find the functions v, with index n> 1. c. (4/10) Find the coefficients cn, with...
Consider the following two lotterics: L $200 with probability 0.7, 0 with probability 0.3, and L' $1200 with probability 0.1 and $0 with probability 0.9. Let xi and ru be the sure amounts of money the individ- ual finds indifferent to L and L' respectively. Show that if preferences are monoton e, the individual must prefer L to L' if and only if L>x