Related papers: Classical non mass preserving solutions of coagula…
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…
In this paper we prove the existence of global classical solutions to continuous coagulation-fragmentation equations with unbounded coefficients under the sole assumption that the coagulation rate is dominated by a power of the…
We prove well-posedness of global solutions for a class of coagulation equations which exhibit the gelation phase transition. To this end, we solve an associated partial differential equation involving the generating functions before and…
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.…
The multicomponent coagulation equation is a generalisation of the Smoluchowski coagulation equation in which size of a particle is described by a vector. As with the original Smoluchowski equation, the multicomponent coagulation equation…
Gelation in the Smoluchowski coagulation equation is commonly interpreted as a finite-time singularity marked by mass loss or moment divergence. We instead characterize gelation as a loss of dynamical stability of the Smoluchowski flow,…
We study a spatially inhomogeneous coagulation model that contains a transport term in the spatial variable. The transport term models the vertical motion of particles due to gravity, thereby incorporating their fall into the dynamics.…
In this article, the existence of mass-conserving solutions is investigated to the continuous coagulation and collisional breakage equation with singular coagulation kernels. Here, the probability distribution function attains singularity…
We consider coagulation equations of Smoluchowski or Flory type where the total merge rate has a bilinear form $\pi(y)\cdot A\pi(x)$ for a vector of conserved quantities $\pi$, generalising the multiplicative kernel. For these kernels, a…
The possible occurrence of instantaneous gelation to Oort-Hulst-Safronov (OHS) coagulation equation is investigated for a certain class of unbounded coagulation kernels. The existence of instantaneous gelation is confirmed by showing the…
Global weak solutions to the continuous Smoluchowski coagulation equation (SCE) are constructed for coagulation kernels featuring an algebraic singularity for small volumes and growing linearly for large volumes, thereby extending previous…
We consider a coagulation multiple-fragmentation equation, which describes the concentration $c\_t(x)$ of particles of mass $x \in (0,\infty)$ at the instant $t \geq 0$ in a model where fragmentation and coalescence phenomena occur. We…
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…
In this article we will investigate the large time behavior of solutions of a special class of initial/boundary value problems that involve nonlinear damped beam equations. We will show that the solution energies of global pseudo classical…
The presence of the aging phenomenon in the homogeneous cooling state (HCS) of a granular fluid composed of inelastic hard spheres or disks is investigated. As a consequence of the scaling property of the $N$-particle distribution function,…
Colloidal gels are widely applied in industry due to their rheological character -- no flow takes place below the yield stress. Such property enables gels to maintain uniform distribution in practical formulations; otherwise, solid…
In this paper, existence and uniqueness of solutions to a non-linear, initial value problem is studied. In particular, we consider a special type of problem which physically represents the time evolution of particle number density resulted…
The critical coagulation-fragmentation equation with multiplicative coagulation and constant fragmentation kernels is known to not have global mass-conserving solutions when the initial mass is greater than $1$. We show that for any given…
Wet granular materials are characterized by a defined bond energy in their particle interaction such that breaking a bond implies an irreversible loss of a fixed amount of energy. Associated with the bond energy is a nonequilibrium…
Existence of global weak solutions to the continuous Oort-Hulst-Safronov (OHS) coagulation equation is investigated for coagulation kernels capturing a singularity near zero and growing linearly at infinity. The proof mainly relies on a…