2017
DOI: 10.1007/s10440-017-0101-x
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Abstract: In this paper a method to rigorously compute several non trivial solutions of the Gray-Scott reaction-diffusion system defined on a 2-dimensional bounded domain is presented. It is proved existence, within rigorous bounds, of non uniform patterns significantly far from being a perturbation of the homogenous states. As a result, a non local diagram of families that bifurcate from the homogenous states is depicted, also showing coexistence of multiple solutions at the same parameter values. Combining analytical … Show more

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Cited by 7 publications
(5 citation statements)
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“…As said in the Introduction, this work is far from being the first application of this kind of rigorous computational techniques to solve systems of PDEs, see for instance [5,13,16,18,22,23]. Particularly related to our work is the result presented in [10].…”
Section: Remark 22mentioning
confidence: 92%
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“…As said in the Introduction, this work is far from being the first application of this kind of rigorous computational techniques to solve systems of PDEs, see for instance [5,13,16,18,22,23]. Particularly related to our work is the result presented in [10].…”
Section: Remark 22mentioning
confidence: 92%
“…The addition of the s 0 coefficient (which is clearly zero since s = v ) is deliberate, because we see each of the sequence of Fourier coefficients (v k ) k≥0 , (w k ) k≥0 , (p k ) k≥0 and (s k ) k≥0 as an element of 1 ν . Plugging these series expansions into (13) and then projecting back onto the cosine/sine basis, we obtain the following (infinite dimensional) algebraic system…”
Section: Algebraic System In Fourier Spacementioning
confidence: 99%
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“…An advantage of using the mean value theorem in Section 6.3.3 is that, irrespective of the order of the vector field, the radii polynomials are always of order 2. The approach taken in, for example, [12] and [24] leads to Z 2 prq bounds whose order depends on the order of the vector field. Our bounds are slightly less sharp due to our central goal of universal applicability, and they remain sufficiently effective in practice.…”
Section: Remark 8 the Interpolations Chosen In The Definitions Of G Kmentioning
confidence: 99%