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Solving large classes of nonlinear systems of PDEs. (English) Zbl 1130.35026
Summary: It is shown that large classes of nonlinear systems of PDEs, with possibly associated initial and/or boundary value problems, can be solved by the method of order completion. The solutions obtained can be assimilated with Hausdorff-continuous functions. The usual Navier-Stokes equations, as well as their various modifications aiming at a realistic modeling, are included as particular cases. The same holds for the critically important constitutive relations in various branches of Continuum Mechanics. The solution method does not involve functional analysis, nor various Sobolev or other spaces of distributions or generalized functions. The general and type independent existence and regularity results regarding solutions presented here have recently been introduced in the literature.
35G20General theory of nonlinear higher-order PDE
35A25Other special methods (PDE)