Related papers: Mass-conserving solutions to coagulation-fragmenta…
In this paper, we consider a class of nonlinear Choquard equations with critical growth, and we show the existence of solutions of the equations. Besides, we consider the corresponding minimizing problem and prove the existence of a…
The problem of the flow trough a porous media is formulated in terms of a pressure equation, based on arguments of volume conservation which state the mechanical equilibrium between the solid and the fluid phases. In the resulting governing…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
The scaling properties of the cluster size distribution of a system of diffusing clusters is studied in terms of a simple kinetic mean field model. It is shown that a one parameter family of mathematically valid scaling solutions exists.…
We prove uniqueness of measure solutions for a multi-component version of Smoluchowski's coagulation equation. The result is valid for a broad range of coagulation kernels and allows to include a source term. The classical coagulation…
We present a model for sticky particles in which cluster sizes after a reaction have $\ell$ fewer total particles than the sum of their reactants. The finite particle system is modeled as a Markov process under a mean-field assumption for…
The mass and size distributions are the key characteristics of any astrophysical objects, including the densest clumps comprising the cold phase of multiphase environments. In our recent papers, we showed how individual clouds of various…
We are concerned with the Sinh-Gordon equation in bounded domains. We construct blow up solutions with residual mass exhibiting either partial or asymmetric blow up, i.e. where both the positive and negative part of the solution blow up.…
The spatial discretization of convective terms in compressible flow equations is studied from an abstract viewpoint, for finite-difference methods and finite-volume type formulations with cell-centered numerical fluxes. General conditions…
We develop a coagulation-fragmentation model to study a system composed of a small number of stochastic objects moving in a confined domain, that can aggregate upon binding to form local clusters of arbitrary sizes. A cluster can also…
We investigate the kinetics of many-species systems with aggregation of similar species clusters and annihilation of opposite species clusters. We find that the interplay between aggregation and annihilation leads to rich kinetic behaviors…
In this paper,for a given conservative solution, we introduce a set of auxiliary variables tailored to this particular solution, and prove that these variables satisfy a particular semilinear system having unique solutions. In turn, we get…
We investigate an integro-differential equation that models the evolution of fragmenting clusters. We assume cluster size to be a continuous variable and allow for situations in which mass is not necessarily conserved during each…
For a nonlinear Schr\"odinger system with mass critical exponent, we prove the existence and orbital stability of standing-wave solutions obtained as minimizers of the underlying energy functional restricted to a double mass constraint. In…
We consider log-convex sequences that satisfy an additional constraint imposed on their rate of growth. We call such sequences log-balanced. It is shown that all such sequences satisfy a pair of double inequalities. Sufficient conditions…
It is proven that the center of mass (COM or Kohn) oscillation of a many-body system in a harmonic trap coincides with the motion of a single particle as long as conserving approximations are applied to treat the interactions. The two…
The large time behavior of non-negative weak solutions to a thin film approximation of the two-phase Muskat problem is studied. A classification of self-similar solutions is first provided: there is always a unique even self-similar…
This note aims at demonstrating the advantage of moving-water well-balanced schemes over still-water well-balanced schemes for the shallow water equations. We concentrate on numerical examples with solutions near a moving-water equilibrium.…
Two numerical algorithms for analyzing planar central and balanced configurations in the $(n+1)$-body problem with a small mass are presented. The first one relies on a direct solution method of the $(n+1)$-body problem by using a…
Using the quantum molecular dynamics model, we study the role of mass asymmetry of colliding nuclei on the fragmentation at the balance energy and on its mass dependence. The study is done by keeping the total mass of the system fixed as…