Oberguggenberger M.B., Rosinger E.E. (Eds.) Solution of Continuous Nonlinear PDEs Through Order Completion

Elsevier, Academic Press, 1994. — 446 p.Dedication
Foreword
General Existence of Solutions Theory
Introduction
Approximation of Solutions of Continuous Nonlinear PDEs
Spaces of Generalized Functions
Extending T(x, D) to the Order Completion of Spaces of Smooth Functions
Existence of Generalized Solutions
A Few First Examples
Generalized Solutions as Measurable Functions
Applications to Specific Classes of Nonlinear and Linear PDEs
The Cauchy Problem for Nonlinear First Order Systems
An Abstract Existence Result
PDEs with Sufficiently Many Smooth Solutions
Nonlinear Systems with Measures as Initial Data
Solution of PDEs and the Completion of Uniform Spaces
Partial Orders Compatible with a Nonlinear Partial Differential Operator
Miscellaneous Results
Group Invariance of Global Generalized Solutions of Nonlinear PDEs
Introduction
Group Invariance of Global Generalized Solutions of Nonlinear PDEs Obtained Through the Algebraic Method
Group Invariance of Generalized Solutions Obtained Through the Algebraic Method : An Alternative Approach
Group Invariance of Global Generalized Solutions Obtained Through the Order Completion Method
Appendix. MacNeille Order Completion Through Dedekind Cuts and Related Results
References
Index