Existence of a global weak solution to the nonlinear waterhammer program
Abstract
The existence of global weak solutions to an initial boundary value problem for a nonlinear hyperbolic system which models fluid flow in a pipe is proven. The effect of friction is modeled by adding a quadratic zero order term to the system of conservation laws for compressible, frictionless flow. Priori bounds are obtained by means of a nonincreasing functional that is compatible with the friction effects. The boundary values for this problem cannot be imposed weakly, so results on the regularity of the solution at the boundary are given.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 December 1981
 Bibcode:
 1981STIN...8233678L
 Keywords:

 Boundary Value Problems;
 Flow Resistance;
 Hyperbolic Functions;
 Nonlinear Systems;
 Pipe Flow;
 Conservation Laws;
 Mathematical Models;
 Quadratic Programming;
 Fluid Mechanics and Heat Transfer