Abstract
We study the global (in time) existence of nonnegative solutions of the Gierer-Meinhardt system with mixed boundary conditions. In the research, the Robin boundary and Neumann boundary conditions were used on the activator and the inhibitor conditions respectively. Based on the priori estimates of solutions, the considerable results were obtained.
Highlights
Biological spatial pattern formation is one area in applied mathematics undergoing vivid investigations in recent years
We study the global existence of nonnegative solutions of the Gierer-Meinhardt system with mixed boundary conditions
The Robin boundary and Neumann boundary conditions were used on the activator and the inhibitor conditions respectively
Summary
Biological spatial pattern formation is one area in applied mathematics undergoing vivid investigations in recent years. The distinctive attribute of Turing’s approach was the role of autocatalysis in coexistence with lateral inhibition These studies led to the assumption of the existence of two chemical substances known as the activator and the inhibitor [2] [3]. In [9], Jiang improved the net self-activation index noted in [5] to ( p −1) r < 1 and showed that the solutions exists globally in time. In this paper we consider the Robin boundary condition (a ≠ 0) on the activator and Neumann boundary condition on the inhibitor and study the global (in time) existence of solutions for the Gierer-Meinhardt system in (1).
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