Existence and uniqueness of a linear hyperbolic initialboundary value problem and the practical application to problems from hydraulics. I  Existence and uniqueness of the linear hyperbolic initialboundary value problem
Abstract
Linear hyperbolic initialboundary value problems arise in connection with a number of physical problems, related to wave propagation involving highly and weakly compressible fluids in pipes, linear transversal and torsional vibrations of rods, and the propagation of electromagnetic waves in homogeneous nonconducting media. An investigation is conducted concerning the existence and uniqueness of the solution of the inhomogeneous hyperbolic initialboundary value problem, taking into account the classical solution. The compatibility conditions are examined in this connection. The compatibility conditions of order zero, the first order, and higher order are equations which are valid along the lines corresponding to the x,y characteristics. It is shown that the derived solution is the only possible solution for the considered problem.
 Publication:

Zeitschrift Angewandte Mathematik und Mechanik
 Pub Date:
 August 1978
 DOI:
 10.1002/zamm.19780580807
 Bibcode:
 1978ZaMM...58..343I
 Keywords:

 Boundary Value Problems;
 Existence Theorems;
 Hydraulics;
 Hyperbolic Differential Equations;
 Linear Equations;
 Uniqueness Theorem;
 Cauchy Problem;
 Compressible Flow;
 Electromagnetic Wave Transmission;
 Pipe Flow;
 Vibration Mode;
 Wave Propagation;
 Fluid Mechanics and Heat Transfer