A singular Gierer—Meinhardt system with different source terms*

@article{Ghergu2008ASG,
  title={A singular Gierer—Meinhardt system with different source terms*},
  author={Marius Ghergu and Vicentiu D. Rădulescu},
  journal={Proceedings of the Royal Society of Edinburgh: Section A Mathematics},
  year={2008},
  volume={138},
  pages={1215 - 1234}
}
We study the existence and non-existence of classical solutions to a general Gierer—Meinhardt system with Dirichlet boundary condition. The main feature of this paper is that we are concerned with a model in which both the activator and the inhibitor have different sources given by general nonlinearities. Under some additional hypotheses and in the case of pure powers in nonlinearities, regularity and uniqueness of the solution in one dimension is also presented. 
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In this paper we study ground-states of the Gierer & Meinhardt system on the line, namely solutions of the problem We prove that given any number N, there exists a solution to this problem exhibiting…
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Abstract Numerical computations often show that the Gierer–Meinhardt system has stable solutions which display patterns of multiple interior peaks (often also called spots). These patterns are also…
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