Well-posedness and qualitative behaviour of a semi-linear parabolic Cauchy problem arising from a generic model for fractional-order autocatalysis

摘要: In this paper, we examine a semi-linear parabolic Cauchy problem with non-Lipschitz nonlinearity which arises as generic form in significant number of applications. Specifically, obtain well-posedness result and the qualitative structure solution detail. The standard classical approach to establishing is precluded owing lack Lipschitz continuity for nonlinearity. Here, existence uniqueness solutions established via recently developed class (Meyer & Needham 2015 partial differential equations. London Mathematical Society Lecture Note Series, vol. 419) examines difference maximal minimal problem. From result, Meyer allows development comparison then used exhibit global continuous dependence on suitable initial dataset. results obtained here are novel This specifically study one-step autocatalytic reaction, schematically given by A→B at rate apbq (where b concentrations A B, respectively, 0