free boundary condition
- To: mathgroup at smc.vnet.net
- Subject: [mg73306] free boundary condition
- From: "Ferdinand" <Ferdinand.Cap at aon.at>
- Date: Sun, 11 Feb 2007 01:12:52 -0500 (EST)
Hi, could someone help to solve with MATHEMATICA the following boundary value problem of 2 part diff equ: 1. the equations : Laplacian[U[x,y,z,t]]=0 and D[U[x,y,z,t],t] +0.5*Grad[U[x,y,z,t]]^2+g*S[x,y,t] =0, g is a const. The unknown functions are : U[x,y,z,t} and S[x,y,t] 2.initial condition: S[0,0,0]=0.5 3.bounday conditions: 3.1 fixed : D[U[x,y,z,t],x]*D[h[x,y],x]+D[U[x,y,z,t],y]*D[h[x,y],y] +D[U[x,y,z,t],z]=0 at z=-h[x,y], where h[x,y] is a numerically given function. 3.2 free Boundary, determined by the solution of the two PDE: D[U[x,y,z,t],z]-D[S[x,y,t],t]-D[U[x,y,z,t},x]*D[S[x,y,t],x]- D[u[x,y,z,t],y]*D[S[x,y,t],y]=0 at z= S[x,y,t] Thanks. F Cap