The discussion focuses on finding the Riemann function for the second-order hyperbolic partial differential equation (PDE) given by the equation uxy + xyux = 0 in the region where x + y > 0. The proposed Riemann function, R(x,y;s,n), must satisfy specific conditions including Rxy - (xyR)x = 0, Rx = 0 on y = n, and Ry = xyR on x = s. A particular solution is derived by setting g(y) = 0, leading to the expression R = exp(xy²/2) H(x), where H(x) is an arbitrary function of x.
PREREQUISITESMathematicians, physicists, and engineering students focusing on applied mathematics, particularly those working with hyperbolic partial differential equations and boundary value problems.
Kate2010 said:Homework Statement
Find the Riemann function for
uxy + xyux = 0, in x + y > 0
u = x, uy = 0, on x+y = 0
Homework Equations
The Attempt at a Solution
I think the Riemann function, R(x,y;s,n), must satisfy:
0 = Rxy - (xyR)x
Rx = 0 on y =n
Ry = xyR on x = s
R = 1 at (x,y) = (s,n)
But I don't know how to solve this beyond just spotting a solution.