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GENERALIZED SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

ROSINGER, E.E.

During the last few years, several fairly systematic nonlinear theories of generalized solutions of rather arbitrary nonlinear partial differential equations have emerged. The aim of this volume is to offer the reader a sufficiently detailed introduction to two of these recent nonlinear theories which have so far contributed most to the study of generalized solutions of nonline...

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NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS: SEQUENTIAL AND WEAK SOLUTIONS

ROSINGER, ELEMER E.

Nonlinear partial differential equations ...

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NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS: AN ALGEBRAIC VIEW OF GENERALIZED SOLUTIONS

ROSINGER, E.E.

A massive transition of interest from solving linear partial differential equations to solving nonlinear ones has taken place during the last two or three decades. The availability of better computers has often made numerical experimentations progress faster than the theoretical understanding of nonlinear partial differential equations. The three most important nonlinear phenom...

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SOLUTION OF CONTINUOUS NONLINEAR PDES THROUGH ORDER COMPLETION

OBERGUGGENBERGER, M.B. / ROSINGER, E.E.

This work inaugurates a new and general solution method for arbitrary continuous nonlinear PDEs. The solution method is based on Dedekind order completion of usual spaces of smooth functions defined on domains in Euclidean spaces. However, the nonlinear PDEs dealt with need not satisfy any kind of monotonicity properties. Moreover, the solution method is completely type inde...

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