We consider self-similar solutions of Smoluchowskiʼs coagulation equation with a diagonal kernel of homogeneity . We show that there exists a family of second-kind self-similar solutions with power-law behavior as with . To our knowledge this is the first example of a non-solvable kernel for which the existence of such a family has been established.
Nous considérons des solutions autosimilaires de lʼéquation de coagulation de Smoluchowski avec un noyau diagonal dʼhomogénéité . Nous prouvons lʼexistence dʼune famille de solutions autosimilaires de deuxième type avec comportement à lʼinfini en puissance , . A notre connaissance, ceci constitue le premier exemple dʼexistence dʼune telle famille pour un noyau non explicitement résoluble.
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Barbara Niethammer 1; Juan J.L. Velázquez 2
@article{CRMATH_2011__349_9-10_559_0, author = {Barbara Niethammer and Juan J.L. Vel\'azquez}, title = {Self-similar solutions with fat tails for a coagulation equation with diagonal kernel}, journal = {Comptes Rendus. Math\'ematique}, pages = {559--562}, publisher = {Elsevier}, volume = {349}, number = {9-10}, year = {2011}, doi = {10.1016/j.crma.2011.03.017}, language = {en}, }
TY - JOUR AU - Barbara Niethammer AU - Juan J.L. Velázquez TI - Self-similar solutions with fat tails for a coagulation equation with diagonal kernel JO - Comptes Rendus. Mathématique PY - 2011 SP - 559 EP - 562 VL - 349 IS - 9-10 PB - Elsevier DO - 10.1016/j.crma.2011.03.017 LA - en ID - CRMATH_2011__349_9-10_559_0 ER -
Barbara Niethammer; Juan J.L. Velázquez. Self-similar solutions with fat tails for a coagulation equation with diagonal kernel. Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 559-562. doi : 10.1016/j.crma.2011.03.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.03.017/
[1] Rigorous results in the scaling theory of irreversible aggregation kinetics, J. Nonl. Math. Phys., Volume 47 (2006) no. 4, p. 042901
[2] Approach to self-similarity in Smoluchowskiʼs coagulation equations, Comm. Pure Appl. Math., Volume 57 (2004), pp. 1197-1232
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