Lord Kelvin's method of images

The theory of semigroups of linear operators and its close relative, the theory of operator cosine functions is an advanced, modern language for differential equations in Banach spaces. The latter equations in turn are often used to model complicated, involved phenomena of microbiology, population genetics, systems biology, population biology etc. Hence, mathematics aids in deeper understanding of biology and, on the other hand, biology inspires development of mathematics.
 

The project aims at systematic research devoted to Lord Kelvin's method of images; it is in the applied mathematics that the renewed interest in the method witnessed recently has it roots. The method is a very practical means of proving that a given operator generates a semigroup of operators or an operator cosine family (hence, it describes a biological process) also in the situation where the classical Hille--Yosida theorem is hard to apply.