please explain in detail, thank you Solve the Cauchy problem for the diffusion equation ut =...
(1 point) Solve the nonhomogeneous heat problem ut = Uxx + sin(3x), 0 < x < 1, u(0,t) = 0, u1,t) = 0 u(x,0) = 2 sin(4x) u(x, t) = Steady State Solution limt-001(x, t) = ((sin(3x))/9)
1. Solve the Cauchy problem (2.1)-(2.2) for the following initial condition a) $(x) = 1 if |2<1 and $(x) = 0 if |z| > 1. b) p(x) = e-x, x > 0; $(x) = 0, x < 0. with the heat, or diffusion, equation on the real line. That is, we We begin with the hea sider the initial value problem Ut = kuxx, XER, t > 0, u(x,0) = 0(2), XER. (2.1) (2.2)
1 point) Solve the nonhomogeneous heat problem ut=uxx+4sin(2x), 0<x<π,ut=uxx+4sin(2x), 0<x<π, u(0,t)=0, u(π,t)=0u(0,t)=0, u(π,t)=0 u(x,0)=5sin(5x)u(x,0)=5sin(5x) u(x,t)=u(x,t)= Steady State Solution limt→∞u(x,t)=limt→∞u(x,t)= Please show all work. (1 point) Solve the nonhomogeneous heat problem Ut = Uxx + 4 sin(2x), 0< x < , u(0,1) = 0, tu(T, t) = 0 u(x,0) = 5 sin(52) u(a,t) Steady State Solution limt u(x, t) = Note: You can earn partial credit on this problem. Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts...
Solve the wave equation on the domain 0 < x < , t > 0 ? uxx Utt = with the boundary condition u (0, t) = 0 and the initial conditions u (x,0) = x2 u (x,0) = x
Please show all steps in detail and as legible as possible. Thank you!!! Consider the two dimensional diffusion of heat in a rectangular section of tissue. Specifically solve for the temperature field, u(x,y,t), in the rectangular section with dimensions having (0<x < a) and (0<y < b), which is governed by the following initial-value, boundary-value problem, where a is a constant: (0,y,t) = 0 uy (x,0,t) = 0 14. (a,y,t) = 0 u(x,b,t)-0 11 (x, y,0) = f(x, y) Consider...
4. (*) Solve the Cauchy problem Ut = 3Uxx, X E R, t> 0, u(x,0) = Q(x), x E R, for the following initial conditions and write the solutions in terms of the erf function. LS 2, -4 < x < 5 (a) $(x) = { 0, otherwise. (b) (x) = e-la-11 Note: In (b) complete the square with respect to y in the exponent of e to obtain a nice form. You need to split your integral based on...
Solve the heat problem ut=uxx−cos(x), 0<x<π, ut=uxx−cos(x), 0<x<π, ux(0,t)=0, ux(π,t)=0 ux(0,t)=0, ux(π,t)=0 u(x,0)=1u(x,0)=1 u(x,t)= ?
please explain all, thanks Fourier Transforms, please explain in detail Solve the following integral equations for an unknown function f(x): (a) exp(-at?) f (x – t)dt = exp(-bx2) b> a > 0 f(t)dt (b) Sca 2 b> a > 0 (x-t)2 +a? 22 +62
PDE problem diffusion equation Solve the diffusion equation in the disk of radius a, with u = t 0, where B is constant B on the boundary and u = 0 when Solve the diffusion equation in the disk of radius a, with u = t 0, where B is constant B on the boundary and u = 0 when