THE LAGRANGE-RIEMANN METHOD FOR INTEGRATION OF QUASILINEAR PARTIAL DIFFERENTIAL EQUATIONS
A new approach to the solution of quasilinear nonelliptic systems of inhomogeneous pde's is given. It is based on the method of Riemann invariants and on the Lagrange idea of variation of constants. An inhomogeneous system of quasilinear equations with coefficients depending on independent and dependent variables and with the right hand side depending only on the dependent variables is transformed, using the Lagrange idea to a homogeneous system (with coefficients depending on independent and on dependent variables) which is solved by a generalized Riemann invariants method. AMS subject classifications (1980). Primary 35L60; Secondary 35A30.