Special Session 138: Differential Equations and Applications to Biology
Invariant sets under semiflows via a Lie--Trotter product formula for semilinear evolution equations
Kamal Khalil
LMAH, University of Le Havre Normandie, FR-CNRS-3335, ISCN, Le Havre 76600, France. France
Co-Author(s): Arnaud Ducrot & Ousmane Seydi
Abstract:
Using a Lie--Trotter product formula for local semiflows, we derive sufficient conditions for the invariance of closed convex sets for a class of semilinear parabolic evolution equations in Banach spaces. As an application, we study a coupled diffusion--advection--reaction system and provide concrete assumptions on the initial data ensuring the invariance of prescribed convex regions. In particular, the obtained criteria guarantee positivity and uniform bounds for solutions within this class.