Finite-time blow-up and blow-up rates for the Gierer–Meinhardt system

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Abstract

  • In this paper, we consider the Gierer–Meinhardt system (1.1), shown below, on a bounded smooth domain (Formula presented.) ((Formula presented.)) with a homogeneous Neumann boundary condition. Under suitable conditions on the exponents (Formula presented.), (Formula presented.), (Formula presented.), and (Formula presented.), we establish sufficient conditions for finite-time blow-up and obtain blow-up rates for blow-up solutions. This work is a continuation of our earlier result in this direction. The Gierer–Meinhardt system was introduced in to model activator–inhibitor systems in pattern formation in ecological systems.
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    Keywords

  • blow-up rate, finite-time blow-up, Gierer–Meinhardt system, reaction–diffusion system
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    Author List

  • Zou H