Solution of Continuous Nonlinear Pdes Through

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 independent. In other words, it does not assume anything about the nonlinear PDEs, except for the continuity of their left hand term, which includes the unkown function. Furthermore the right hand term of such nonlinear PDEs can in fact be given any discontinuous and measurable function.

General Existence of Solutions Theory	p. 1
Approximation of Solutions of Continuous Nonlinear PDEs	p. 11
Spaces of Generalized Functions	p. 24
Extending T(x,D) to the Order Completion of Spaces of Smooth Functions	p. 31
Existence of Generalized Solutions	p. 38
A Few First Examples	p. 65
Generalized Solutions as Measurable Functions	p. 74
Applications to Specific Classes of Linear and Nonlinear PDEs	p. 159
The Cauchy Problem for Nonlinear First Order Systems	p. 161
An Abstract Existence Result	p. 184
PDEs with Sufficiently Many Smooth Solutions	p. 195
Nonlinear Systems with Measures as Initial Data	p. 210
Solution of PDEs and the Completion of Uniform Spaces	p. 237
Partial Orders Compatible with a Nonlinear Partial Differential Operator	p. 263
Group Invariance of Global Generalized Solutions of Nonlinear PDEs	p. 295
Group Invariance of Global Generalized Solutions of Nonlinear PDEs Obtained Through the Algebraic Method	p. 299
Group Invariance of Generalized Solutions Obtained Through the Algebraic Method : An Alternative Approach	p. 354
Group Invariance of Global Generalized Solutions Obtained Through the Order Completion Method	p. 365
Appendix	p. 389
References	p. 421
Index	p. 429
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Solution of Continuous Nonlinear Pdes Through Order Completion

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