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My research area is age structure modelling, basically when applied to reaction diffusion equations. We mainly discuss the existence of travelling wave solutions; I want to work on the stability of travelling wave solutions.

Where should I read about this topic and how should I proceed? I am totally stuck.

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    $\begingroup$ Such matters are best discussed with your research mentor, who normally is an expert and knows the context. If a mentor isn't an expert, as may happen if you picked the topic yourself, then the fact that you are "totally stuck" suggests you may be better off switching to a project within mentor's expertise. $\endgroup$
    – Igor Belegradek
    Commented May 20, 2022 at 13:45

1 Answer 1

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As stated by Igor Belegradek in his comment above, the first thing to do is to search for an expert advice. However, an expert advice is sometimes hard to find, for example if you work in a big firm and you work on a research project involving strict confidentiality policies. Therefore a reference is useful, at least to see what kind of research have been done on the topic of interest: and, on the theory of traveling waves in for reaction diffusion equations, my advice is to have a look at the the monograph [1]. It is a really wonderful work as it details the theory and the history of the topic: written by chemical engineers highly skilled in mathematics, it is still a true reference, despite being written nearly 28 years ago.

Reference

[1] Aizik Isaakovich Vol’pert, Vitaly Aizikovich Vol’pert, Vladimir Aizikovich Vol’pert, Traveling wave solutions of parabolic systems, (English) Translations of Mathematical Monographs, 140. Providence, RI: American Mathematical Society. xii, 448 p. (1994), MR1297766, Zbl 1001.35060.

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