Related papers: Global classical solutions to the continuous coagu…
This paper focuses on the study of existence and uniqueness of distributional and classical solutions to the Cauchy Boltzmann problem for the soft potential case assuming $S^{n-1}$ integrability of the angular part of the collision kernel…
In this paper we construct classical solutions of a family of coagulation equations with homogeneous kernels that exhibit the behaviour known as gelation. This behaviour consists in the loss of mass due to the fact that some of the…
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…
A mathematical model for the continuous nonlinear fragmentation equation is considered in the presence of mass transfer. In this paper, we demonstrate the existence of mass-conserving weak solutions to the nonlinear fragmentation equation…
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 the global existence and uniform-in-time bounds of classical solutions in all dimensions to reaction-diffusion systems dissipating mass. By utilizing the duality method and the regularization of the heat operator, we show that if…
The existence of weak solutions to the continuous coagulation equation with multiple fragmentation is shown for a class of unbounded coagulation and fragmentation kernels, the fragmentation kernel having possibly a singularity at the…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…
The goal of this work is to establish the global existence of nonnegative classical solutions in all dimensions for a system of highly nonlinear reaction-diffusion equations. We address the case for different diffusion coefficients and 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 the question of global existence of smooth solutions to a multi-species aggregation-diffusion equation for a class of singular interaction kernels. We establish a smallness condition on the initial data which yields global…
In this article we prove the existence of solutions to the singular coagulation equation with multifragmentation. We use weighted $L^1$-spaces to deal with the singularities and to obtain regular solutions. The Smoluchowski kernel is…
In this article we prove the existence of solutions to the coagulation equation with singular kernels. We use weighted L^1-spaces to deal with the singularities in order to obtain regular solutions. The Smoluchowski kernel is covered by our…
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…
The article presents the existence and mass conservation of solution for the discrete Safronov-Dubovski coagulation equation for the product coalescence coefficients $\phi$ such that $\phi_{i,j} \leq ij$ $\forall$ $i,j \in \mathbb{N}$. Both…
In this paper, for compressible Euler equations in multiple space dimensions, we prove the break-down of classical solutions with a large class of initial data by tracking the propagation of radially symmetric expanding wave including…
In this work, we establish the existence of mass-conserving weak solutions to a nonlinear collision-induced breakage equation in which binary collisions may trigger particle breakup. The result is proved for a class of product-type…
Collisional breakage in the particulate process has a lot of recent curiosity. We study the pure collisional breakage equation which is nonlinear in nature accompanied by locally bounded breakage kernel and collision kernel. The continuous…
The now classical replicator equation describes a wide variety of biological phenomena, including those in theoretical genetics, evolutionary game theory, or in the theories of the origin of life. Among other questions, the permanence of…
We consider a collisionless ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, the relativistic Vlasov-Klein-Gordon system, we prove local-in-time existence…