The concept of evolutionary equations encompasses differential equations in finite and infinite dimensions, including delay differential and Volterra integral equations. The main objective of this research is to study the existence, regularity, and asymptotic behaviour of solutions to evolutionary equations, both deterministic and stochastic.
The research on nonlinear parabolic equations concentrates on
The viscosity solution concept has been introduced as a generalization of the classical concept of what is meant by a 'solution' to a partial differential equation (PDE). It has been found that this concept is the natural solution concept for large classes of equations satisfying certain conditions and in these cases it is possible to develop a rather comprehensive theory. The objective of this research is to strengthen, extend, and simplify this theory with special emphasis on the regularity properties of viscosity solutions.