The stationary Gierer-Meinhardt system in the upper half-space: existence, nonexistence and asymptotics (Q6624804)
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scientific article; zbMATH DE number 7932372
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The stationary Gierer-Meinhardt system in the upper half-space: existence, nonexistence and asymptotics |
scientific article; zbMATH DE number 7932372 |
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The stationary Gierer-Meinhardt system in the upper half-space: existence, nonexistence and asymptotics (English)
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28 October 2024
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The purpose of this paper is to study the existence, nonexistence and asymptotics of the steady-states (that is, solutions which are time independent) of the Gierer-Meinhardt system of semilinear PDEs under homogeneous Neumann boundary conditions, when the domain \(\Omega\) is the upper half-space in \(\mathbb R^N_+,\;N\geq 3\). The approach combines integral representations of solutions and various integral estimates with fixed point arguments.
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