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GENERAL QUESTIONS IN THE THEORY OF PARTIAL DIFFEREN
Reduction of Quasilinear Systems of Equations to Normal Form
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arbitrary boundary conditions bounded Cauchy problem characteristic closed region coefficients coincides const constant continuous function continuously differentiable function continuously differentiable solution converges uniformly coordinate origin corresponding curve defined by Eq denote Dirichlet problem domain G double layer eigenfunctions eigenvalues equa example exterior func function f given Green's formula Green's function harmonic functions heat equation independent variables infinity initial conditions instant integral equation interval Laplace's equation linear member of Eq obtain one-dimensional operator orthogonality Ostrogradskiy's formula partial differential equations plane point P0 Poisson's positive number problem for Eq Proof region Q respect Riemann function right-hand member second boundary-value problem Sect single layer solution of Eq space sphere steady-state oscillations Sturm-Liouville problem subsection sufficiently small Suppose surface system of equations takes the form theorem thermal potential third boundary-value problem three-dimensional tion twice continuously differentiable two-dimensional unit source value problem vector wave equation zero