Research on the reaction-diffusion equation with Robin and free boundary condition

Abstract

The free boundary value problem of reaction-diffusion equation is studied. In the first chapter, the Logistic diffusion equation with free boundary and the main work of this paper are introduced. The second chapter is the preparation work, explaining the existence and uniqueness of the solution of the free boundary Logistic diffusion equation. In the third chapter, we prove that messages propagate or disappear in finite time by constructing the asymptotic properties of upper and lower solutions. In chapter 4, the criterion of diffusion disappearance is given, and the threshold of information propagation or disappearance in finite time is given according to the initial value. The results show that when the given value is larger than the threshold value, the information will propagate in the whole region. Otherwise the message will stop propagating for a limited time.

Mathematical Analysis of Reaction Diffusion Equation using Laplace Transform in Life Sciences

“…In 2019, Zhu [11] searched free boundary problems of several types of reaction diffusion systems. In 2021 Ran et al [12] proposed research on the reaction diffusion equation with Robin and free boundary condition. Assaely et al [13] explained full finite element scheme for reaction diffusion systems on embedded curved surface in R3.…”