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It is well-known that the two-dimensional Keller-Segel system admits finite time blowup solutions, which is the case if the initial density has a total mass greater than $8\pi$ and a finite second moment. Several constructive examples of…

Analysis of PDEs · Mathematics 2024-09-10 Charles Collot , Tej-Eddine Ghoul , Nader Masmoudi , Van Tien Nguyen

Intracellular protein patterns are described by (nearly) mass-conserving reaction-diffusion systems. While these patterns initially form out of a homogeneous steady state due to the well-understood Turing instability, no general theory…

Pattern Formation and Solitons · Physics 2024-01-11 Henrik Weyer , Fridtjof Brauns , Erwin Frey

This paper proves the existence of weak solutions to the spatially homogeneous Boltzmann equation for Maxwellian molecules, when the initial data are chosen from the space of all Borel probability measures on R^3 with finite second moments…

Mathematical Physics · Physics 2013-06-24 Emanuele Dolera

Global existence of mild solutions to the discrete collisional breakage equations is established for a broad class of collision kernels, without imposing any growth assumptions. In addition, classical solutions are constructed, and…

Classical Analysis and ODEs · Mathematics 2025-07-10 Mashkoor Ali , Philippe Laurençot

The formation of light nuclei can be described as the coalescence of clusters of nucleons into nuclei. In the case of small interacting systems, such as dark matter and $e^+e^-$ annihilations or $pp$ collisions, the coalescence condition is…

High Energy Physics - Phenomenology · Physics 2021-06-02 M. Kachelriess , S. Ostapchenko , J. Tjemsland

Fragmentation--coagulation processes, in which aggregates can break up or get together, often occur together with decay processes in which the components can be removed from the aggregates by a chemical reaction, evaporation, dissolution,…

Dynamical Systems · Mathematics 2018-11-14 Jacek Banasiak , Luke O. Joel , Sergey Shindin

Abridged. A large fraction of stars are found in binary systems. It is therefore important for our understanding of the star formation process, to investigate the fragmentation of dense molecular cores. We study the influence of the…

Astrophysics · Physics 2009-11-13 P. Hennebelle , R. Teyssier

We prove the existence of weak solutions of a class of multi-species cross-diffusion systems as well as the propagation of chaos result by means of nonlocal approximation of the nonlinear diffusion terms, coupling methods and compactness…

Analysis of PDEs · Mathematics 2024-10-18 Jose Antonio Carrillo , Shuchen Guo

The global existence of mass-conserving weak solutions to the Safronov-Dubovskii coagulation equation is shown for the coagulation kernels satisfying the at most linear growth for large sizes. In contrast to previous works, the proof mainly…

Analysis of PDEs · Mathematics 2023-03-28 Mashkoor Ali , Pooja Rai , Ankik Kumar Giri

In this work, we study the long time asymptotics of a coagulation model which describes the evolution of a system of particles characterized by their volume and surface area. The aggregation mechanism takes place in two stages: collision…

Analysis of PDEs · Mathematics 2024-11-19 Iulia Cristian , Juan J. L. Velázquez

In this paper we study a class of coagulation equations including a source term that injects in the system clusters of size of order one. The coagulation kernel is homogeneous, of homogeneity $\gamma < 1$, such that $K(x,y)$ is…

Analysis of PDEs · Mathematics 2023-10-03 Iulia Cristian , Marina A. Ferreira , Eugenia Franco , Juan J. L. Velázquez

This article deals with the convergence of finite volume scheme (FVS) for solving coagulation and multiple fragmentation equations having locally bounded coagulation kernel but singularity near the origin due to fragmentation rates. Thanks…

Numerical Analysis · Mathematics 2022-10-04 Sanjiv Kumar Bariwal , Prasanta Kumar Barik , Ankik Kumar Giri , Rajesh Kumar

Inertial particles advected in chaotic flows often accumulate in strange attractors. While moving in these fractal sets they usually approach each other and collide. Here we consider inertial particles aggregating upon collision. The new…

Fluid Dynamics · Physics 2009-11-13 Jens C. Zahnow , Rafael D. Vilela , Ulrike Feudel , Tamas Tel

The present paper studies existence and distributional uniqueness of subclasses of stationary hard-core particle systems arising as thinnings of stationary particle processes. These subclasses are defined by natural maximality criteria. We…

Probability · Mathematics 2018-01-17 Christian Hirsch , Günter Last

We study multicomponent coagulation via the Smoluchowski coagulation equation under non-equilibrium stationary conditions induced by a source of small clusters. The coagulation kernel can be very general, merely satisfying certain power law…

Analysis of PDEs · Mathematics 2021-03-25 Marina A. Ferreira , Jani Lukkarinen , Alessia Nota , Juan J. L. Velázquez

We consider the exchangeable fragmentation-coagulation (EFC) processes, where the coagulations are multiple and not simultaneous, as in a $\Lambda$-coalescent, and the fragmentations dislocate at finite rate an individual block into…

Probability · Mathematics 2020-12-18 Clément Foucart , Xiaowen Zhou

We prove boundedness and regularity estimates for weak solutions to a class of linear nonlocal equations involving integro-differential operators with almost no order of differentiability. In particular, we show that bounded weak solutions…

Analysis of PDEs · Mathematics 2025-03-04 Sven Jarohs , Moritz Kassmann , Tobias Weth

We study the asymptotic properties of the steady state mass distribution for a class of collision kernels in an aggregation-shattering model in the limit of small shattering probabilities. It is shown that the exponents characterizing the…

Statistical Mechanics · Physics 2018-02-22 Colm Connaughton , Arghya Dutta , R. Rajesh , Nana Siddharth , Oleg Zaboronski

In this paper, we consider a continuous fragmentation--coagulation model in which the reacting particles can be transported in physical space through either advection or diffusion. We prove new results on the generation of $C_0$-semigroups…

Analysis of PDEs · Mathematics 2026-01-06 Jacek Banasiak , Nduduzo Majozi

This paper deals with the existence and uniqueness of solutions to kinetic equations describing alignment of self-propelled particles. The particularity of these models is that the velocity variable is not on the euclidean space but…

Analysis of PDEs · Mathematics 2023-05-10 Marc Briant , Nicolas Meunier