Review of Some Essentials in Weak Solutions and Distributions. Classical Versus Distribution Solutions. Impossibility and Degeneracy Results in Distributions. Limitations of the Linear Distribution Theory.
Colombeau's Nonlinear Theory of Generalized Functions. The Differential Algebra G as an Extension of the D' Distributions. Generalized Solutions of Nonlinear Partial Differential Equations. Generalized Solutions for Linear Partial Differential Equations.
A Necessary Structure for Nonlinear Theories of Generalized Functions. Stability, Generality and Exactness of Generalized Solutions. Chains of Algebras of Generalized Functions. Resolution of Singularities of Weak Solutions for Polynomial Nonlinear Partial Differential Equations.