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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
- Korteweg-de 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
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