{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:55:04Z","timestamp":1787324104781,"version":"3.56.0"},"reference-count":28,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/100009935","name":"Indo-French Centre for Applied Mathematics","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100009935","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Math. Anal."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>A mathematical model for collision-induced breakage is considered. Existence of weak solutions to the continuous nonlinear collision-induced breakage equation is shown for a large class of unbounded collision kernels and daughter distribution functions, assuming the collision kernel $K$ to be given by $K(x,y)= x^{\\alpha} y^{\\beta} + x^{\\beta} y^{\\alpha}$ with $\\alpha \\le \\beta \\le 1$. When $\\alpha + \\beta \\in [1,2]$, it is shown that there exists at least one weak mass-conserving solution for all times. In contrast, when $\\alpha + \\beta \\in [0,1)$ and $\\alpha \\ge 0$, global mass-conserving weak solutions do not exist, though such solutions are constructed on a finite time interval depending on the initial condition. The question of uniqueness is also considered. Finally, for $\\alpha &lt;0$ and a specific daughter distribution function, the nonexistence of mass-conserving solutions is also established.<\/jats:p>","DOI":"10.1137\/20m1386852","type":"journal-article","created":{"date-parts":[[2021,8,19]],"date-time":"2021-08-19T12:15:31Z","timestamp":1629375331000},"page":"4605-4636","source":"Crossref","is-referenced-by-count":17,"title":["Existence and NonExistence for the Collision-Induced Breakage Equation"],"prefix":"10.1137","volume":"53","author":[{"given":"Ankik Kumar","family":"Giri","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3091-8085","authenticated-orcid":true,"given":"Philippe","family":"Lauren\u00e7ot","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,8,19]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1515\/9783110853698"},{"key":"atypb2","volume-title":"Analytic Methods for Coagulation-Fragmentation Models","author":"Banasiak J.","year":"2019"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511617768"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1503957112"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/BF00916423"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.60.2450"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/23\/7\/028"},{"key":"atypb8","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1090\/S0002-9947-1915-1501024-5","volume":"16","author":"Vall\u00e9e Poussin C. 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