Existence globale pour l'équation de Smoluchowski continue non homogène et comportement asymptotique des solutions

On self-similarity and stationary problem for fragmentation and coagulation models

“…and therefore for a constant C T = C T ( f in L 1 k , a, b, k) for any T > 0 and any k λ. See [34,42] for the former and just copy the proof of Lemma 4.2 for the last ones. A first consequence is that for any given f in ∈ L ∞ with compact support included in (0, ∞), one may build a solution f ∈ C([0, ∞); Y ) satisfying (5.16), see [36], which is unique thanks to Theorem 2.9.…”

Local and global strong solutions to continuous coagulation–fragmentation equations with diffusion

“…Due to (19) it suffices to prove that u → U u ∈ L C (J , L p ), C + −1 (J , H q,B ) for := n(1/p − 1/q)/2 + /2. But (10) implies that, for u ∈ C (J , L p ) and t ∈J ,…”

“…Provided the kernels satisfy some suitable growth and additional structural conditions, global-in-time existence of weak solutions is proven and also their large-time behavior is investigated in a particular situation. Subsequently, the global existence result has been improved in [19] in that also less restrictive structural conditions for the kernels have to be imposed. However, neither of these papers provides uniqueness nor conservation of mass, in general, due to the low regularity of the solutions.…”

Spatial coagulation with bounded coagulation rate

“…They allow linear growth for the coagulation rate. The works [3,[8][9][10], identify different settings in which one can prove the existence of a weak solution to equation (1.1) (in different appropriate senses), defined for all times and for unbounded coagulation kernels controlled in different ways. They all investigate equation (1.1) without convection and with a diffusion of the form (1.2).…”