Asymptotic Stabilization in a Three‐Dimensional Coral Fertilization Model Involving a Stokes Equation and p‐Laplace Diffusion

ABSTRACT

This note is concerned with an initial‐boundary value problem associated with a three‐dimensional chemotaxis‐Stokes system modeling coral fertilization under the effects of ‐Laplace diffusion. Based on an extended lemma which is applicable to warrant decay in superlinearly dampened ordinary differential equalities with inhomogeneities decaying in some temporal average, it is proved that when the global weak solutions of the initial‐boundary value problem will approach to some constant equilibrium. Besides that, quantitative description of temporal convergence to the constant equilibrium has been provided in the case when the sperms and eggs possess different initial mass. This addresses an open issue that has been left in a precedent study merely concentrating on global boundedness of the solutions.