The purpose of this paper is to enhance a correspondence between the dynamics of the differential equations ẏ(t) = g(y(t)) on ℝd and those of the parabolic equations on a bounded domain Ω. We give details on the similarities of these dynamics in the cases d = 1, d = 2 and d ≥ 3 and in the corresponding cases Ω = (0, 1), Ω = 𝕋1 and dim(Ω) ≥ 2 respectively. In addition to the beauty of such a correspondence, this could serve as a guideline for future research on the dynamics of parabolic equations.
Romain Joly 1 ; Geneviève Raugel 1
@article{CML_2011__3_3_471_0,
author = {Romain Joly and Genevi\`eve Raugel},
title = {A striking correspondence between the dynamics generated by the vector fields and by the scalar parabolic equations},
journal = {Confluentes Mathematici},
pages = {471--493},
publisher = {World Scientific Publishing Co Pte Ltd},
volume = {3},
number = {3},
year = {2011},
doi = {10.1142/S1793744211000369},
language = {en},
url = {https://cml.centre-mersenne.org/articles/10.1142/S1793744211000369/}
}
TY - JOUR AU - Romain Joly AU - Geneviève Raugel TI - A striking correspondence between the dynamics generated by the vector fields and by the scalar parabolic equations JO - Confluentes Mathematici PY - 2011 SP - 471 EP - 493 VL - 3 IS - 3 PB - World Scientific Publishing Co Pte Ltd UR - https://cml.centre-mersenne.org/articles/10.1142/S1793744211000369/ DO - 10.1142/S1793744211000369 LA - en ID - CML_2011__3_3_471_0 ER -
%0 Journal Article %A Romain Joly %A Geneviève Raugel %T A striking correspondence between the dynamics generated by the vector fields and by the scalar parabolic equations %J Confluentes Mathematici %D 2011 %P 471-493 %V 3 %N 3 %I World Scientific Publishing Co Pte Ltd %U https://cml.centre-mersenne.org/articles/10.1142/S1793744211000369/ %R 10.1142/S1793744211000369 %G en %F CML_2011__3_3_471_0
Romain Joly; Geneviève Raugel. A striking correspondence between the dynamics generated by the vector fields and by the scalar parabolic equations. Confluentes Mathematici, Tome 3 (2011) no. 3, pp. 471-493. doi : 10.1142/S1793744211000369. https://cml.centre-mersenne.org/articles/10.1142/S1793744211000369/
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