Speaker: Tang Quoc Bao, University of Graz, Austria
Abstract: This talk discusses global existence and boundedness of solutions to reaction-diffusion systems which possess non-negative solutions and a control of the total mass. These two properties are common in many models in biology or chemistry but not sufficient to rule out finite time blow-up. Recent works show that if the nonlinearities are at most quadratic, then the global well-posedness of classical solutions can be ensured. This turns out to be optimal in a certain sense. Possible extensions such as intermediate sum conditions or the case of non-smooth diffusion coefficients are also mentioned.