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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].…”

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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].…”

“…For example equilibria and periodic orbits of ordinary, delay, partial differential equations (PDEs) as well as systems of PDEs are considered in [10,11,12,13,14,15,16,17]. The same approach is applied in order to validate transverse connecting orbits for ordinary differential equations in [18,19,20], to study symmetric pulses, kinks and radially symmetric solutions in reaction diffusion equations [21,22], to solve initial and boundary value problems for ordinary differential equations in a mathematically rigorous way [19,23], and to validate series expansions for the Floquet normal form for linear differential equations with periodic coefficients.…”

“…It was later on adapted to prove existence of equilibria of high-dimensional PDEs (e.g. see [20], [21], [22], [23]), of periodic orbits of delay equations and PDEs (e.g. see [24], [25], [26], [27]) and connecting orbits of ODEs [4].…”