Solution of a class of reaction-diffusion systems via logarithmic   Sobolev inequality
  We study global existence, uniqueness and positivity of weak solutions of a class of reaction-diffusion systems of chemical kinetics type, under the assumptions of logarithmic Sobolev inequality and appropriate exponential integrability of the initial data. 
Pierre Foug\`eres (IMT), Ivan Gentil (ICJ), Boguslaw Zegarlinski
math.PR