Since , so the given partial differential equation can be written as
Determine the solution in the expansion fan. In this problem, we consider the flow of water through a porous medium. Specifically, u, is the water content at depth z and timet measured as a ratio...
In this problem, we consider the flow of water through a porous medium. Specifically, u(r, t) is the water content at depth z and time t measured as a ratio of water-filled pore space to total pore-space. (Thus, 0 Su S1) We assume that u satisfies the conservation law and initial condition (0 t>0 u(x, 0) = 0 n(x, 0) = 1 u(x, 0) = 0 x < 0 0<x<1 x > 1. I. Sketch a plot of the characteristics....
1. Consider the Partial Differential Equation ot u(0,t) = u(r, t) = 0 a(x, 0)-x (Y), sin (! We know the general solution to the Basic Heat Equation is u(z,t)-Σ b e ). n= 1 (b) Find the unique solution that satisfies the given initial condition ur, 0) -2. (Hint: bn is given by the Fourier Coefficients-f(z),sin(Y- UsefulFormulas/Facts for PDEs/Fourier Series 1)2 (TiT) » x sin aL(1)1 a24(부) (TiT) 1)+1 0 1. Consider the Partial Differential Equation ot u(0,t) =...