PDE with boundary condition ODE

*To*: mathgroup at smc.vnet.net*Subject*: [mg50214] PDE with boundary condition ODE*From*: mathma18 at hotmail.com (Narasimham G.L.)*Date*: Sat, 21 Aug 2004 03:04:15 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Beginning attempt to solve for z(x,y)(constant negative Gauss curvature)in Monge form PDE r*t-s^2 == -(1+p^2+q^2)^2, with ODE BC as p(x,0)^2=(1+z^2)/(2-z^2) for boundary y=0 has mixed lists. TIA for help. Clear[x,y,z,z2]; xm=.6; ym=3; pde=-(1+D[z[x, y], x]^2+D[z[x, y], y]^2)^2 == (D[z[x, y],{x,2}]*D[z[x, y],{y,2}]-D[z[x, y],{x,y}]^2); BC= {D[z[x, 0],x]^2 == (1+z[x,0]^2)/(2-z[x,0]^2), z[0, 0]== .01,D[z[x,0],x]==.01}; "flat BC= {z[x,0]==x^2/5}" ; NDSolve[{pde,BC},z,{x,0,xm},{y,0,ym}]; z2[u_,v_]=z[u,v]/.First[%]; Plot3D[z2[x,y],{x,0,xm},{y,0,ym}];