Alex Misiats

Nonlinear stochastic reaction-diffusion equations describe physical and biological processes including heat explosion, tumor growth and evolution of biological species in random environment. In these models one of the important questions is whether the quantity of interest  (e.g. the tumor, the population etc.) stays bounded or continues to grow as time elapses. The answer to this question is far from trivial, even for some simple equations perturbed with random noise. In my works I described a large class of stochastic reaction diffusion equations, for which bounded solutions exist. In some cases these bounded solutions can be easily computed via explicit iteration schemes. I also analysed various numerical schemes for nonlinear Richards equation.