
Differential algebras of generalized functions provide a framework for
unifying and extending existing solution concepts of several important
classes of (linear and) nonlinear PDE. An introduction to this line of
research can be found in M.Oberguggenberger,
Multiplication of distributions
and applications to partial differential equations, Pitman Research Notes
in Mathematics, Vol 259, Longman, Harlow, 1992.
Areas of research
 Semilinear Hyperbolic Systems
 Delta Waves
 Hyperbolic Systems with discontinuous Coefficients
 Strongly Singular Data
 Generalized Solutions
 Quasilinear Hyperbolic Systems
 Shock Waves in Conservative and Nonconservative Systems
 Small Viscosity Limits
 Numerical Methods
 Special Equations with strongly singular Data
 Transport Equations
 Kortewegde Vries and related Equations
 Semilinear Parabolic Equations
 Schrödinger Equations with singular potential
 Regularity Theory
 Pseudodifferential Operators on Algebras of Generalized Functions
 Elliptic Regularity
 Equations with constant generalized Coefficients

