Related papers: Convergence of the discrete Redner-Ben-Avraham-Kah…
The Redner-Ben-Avraham-Kahng (RBK) coagulation model provide a fundamental framework for modeling the aggregation of particles in various physical and biological systems. In this paper, we investigate the global existence of solutions to…
We study the behaviour as $t\to\infty$ of solutions $(c_j(t))$ to the Redner--Ben-Avraham--Kahng coagulation system with positive and compactly supported initial data, rigorously proving and slightly extending results originally established…
We take into account a coagulation model that simulates a distinct kind of dynamics. In this model, two particles collide to produce a single particle, but the resulting particle decreases in size, allowing each particle to be fully…
In this article, we study the passage of limits from discrete to continuous condensing aggregation equation which comprises of Oort-Hulst-Safronov (OHS) equation together with inverse aggregation process. We establish the relation between…
Here, we study a discrete Coagulation-Fragmentation equation with a multiplicative coagulation kernel and a constant fragmentation kernel, which is critical. We apply the discrete Bernstein transform to the original…
Under the condition of detailed balance and some additional restrictions on the size of the coefficients, we identify the equilibrium distribution to which solutions of the discrete coagulation-fragmentation system of equations converge for…
We consider a coagulation model first introduced by Redner, Ben-Avraham and Krapivsky in [Redner, Ben-Avraham, Kahng: Kinetics of 'cluster eating', J. Phys. A: Math. Gen., 20 (1987), 1231-1238], the main feature of which is that the…
In the context of mathematical modeling, it is sometimes convenient to integrate models of different nature. These types of combinations, however, might entail difficulties even when individual models are well-understood, particularly in…
In this paper we derive a constrained Hamilton-Jacobi equation with obstacle from a discrete non-linear integro-differential model of population dynamics, with exponentially decaying mutation kernel. The exponential decay of the kernel…
The Regularised Inertial Dean-Kawasaki model (RIDK) -- introduced by the authors and J. Zimmer in earlier works -- is a nonlinear stochastic PDE capturing fluctuations around the mean-field limit for large-scale particle systems in both…
Solutions of Rough Differential Equations (RDE) may be defined as paths whose increments are close to an approximation of the associated flow. They are constructed through a discrete scheme using a non-linear sewing lemma. In this article,…
In this paper we study the discrete coagulation--fragmentation models with growth, decay and sedimentation. We demonstrate the existence and uniqueness of classical global solutions provided the linear processes are sufficiently strong.…
We study a class of processes that are akin to the Wright-Fisher model, with transition probabilities weighted in terms of the frequency-dependent fitness of the population types. By considering an approximate weak formulation of the…
It is by now well-known that one can recover a potential in the wave equation from the knowledge of the initial waves, the boundary data and the flux on a part of the boundary satisfying the Gamma-conditions of J.-L. Lions. We are…
This work develops a convergence theory for H(div)-conforming finite element methods applied to the steady Oseen problem, focusing on cases where the exact finite element complex holds while the commuting diagram property may fail. The…
New model equations are derived for dynamics of self-aggregation of finite-size particles. Differences from standard Debye-Huckel and Keller-Segel models are: the mobility of particles depends on the configuration of their neighbors and…
A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum…
We study the equilibrium fluctuations of an interacting particle system evolving on the discrete ring with $N\in\mathbb N$ points, denoted by $\mathbb T_N$, and with three species of particles that we name $A,B$ and $C$, but such that at…
In this paper we study the continuous coagulation and multiple fragmentation equation for the mean-field description of a system of particles taking into account the combined effect of the coagulation and the fragmentation processes in…
This article reports on the confluence of two streams of research, one emanating from the fields of numerical analysis and scientific computation, the other from topology and geometry. In it we consider the numerical discretization of…