Related papers: Existence and Non-existence for Exchange-Driven Gr…
We consider a model of cell motion with boundary signal production which describes some aspects of eukaryotic cell migration. Generic polarity markers located in the cell are transported by actin which they help to polymerize. This leads to…
In this article, the existence of global classical solutions to the discrete coagulation equations with collisional breakage is established for collisional kernel having linear growth whereas the uniqueness is shown under additional…
A competitive growth model (CGM) describes aggregation of a single type of particle under two distinct growth rules with occurrence probabilities $p$ and $1-p$. We explain the origin of scaling behaviors of the resulting surface roughness…
We introduce and analyze a nonlinear exchange dynamics for Ising spin systems with arbitrary interactions. The evolution is governed by a quadratic Boltzmann-type equation that conserves the mean magnetization. Collisions are encoded…
This paper deals with the two-species Keller--Segel-Stokes system with competitive kinetics $(n_1)_t + u\cdot\nabla n_1 =\Delta n_1 - \chi_1\nabla\cdot(n_1\nabla c)+ \mu_1n_1(1- n_1 - a_1n_2)$, $(n_2)_t + u\cdot\nabla n_2 =\Delta n_2 -…
Interaction graphs, such as those recording emails between individuals or transactions between institutions, tend to be sparse yet structured, and often grow in an unbounded manner. Such behavior can be well-captured by structured,…
A class of energy-transport equations without electric field under mixed Dirichlet-Neumann boundary conditions is analyzed. The system of degenerate and strongly coupled parabolic equations for the particle density and temperature arises in…
By using a time-dependent operator converting a distribution function (statistical operator) of a total system under consideration into the relevant form, new exact nonlinear generalized master equations (GMEs) are derived. The…
We study existence, uniqueness, norm estimates and asymptotic time behaviour (in some cases can be claimed to be sharp) for the solution of a general evolutionary integral (differential) equation of scalar type on a locally compact…
We consider the Euler alignment system with mildly singular interaction kernels. When the local repulsion term is of the fractional type, global in time existence of smooth solutions was proved…
In this research, we would like to study the global (in time) existence of small data solutions to the following damped $\sigma$-evolution equations with nonlocal (in space) nonlinearity: \begin{equation*}…
Multi-species reaction-diffusion systems, with more-than-two-site interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time…
The phenomenon of group cooperation constitutes a fundamental mechanism underlying various social and biological systems. Complex networks provide a structural framework for group interactions, where individuals can not only obtain…
In this paper we consider the following nonlocal autonomous evolution equation in a bounded domain $\Omega$ in $\mathbb{R}^N$ \[ \partial_t u(x,t) =- h(x)u(x,t) + g \Big(\int_{\Omega} J(x,y)u(y,t)dy \Big) +f(x,u(x,t)) \] where $h\in…
We introduce and analyse a mathematical model describing the dynamics of particles generated by charge-exchange interactions. The model extends the well-established exchange-driven growth model, previously studied in several works, by…
We prove the existence and uniqueness of global smooth solutions of the critical dissipative SQG equation in bounded domains in $\mathbb R^2$. This solves an open problem. We introduce a new methodology of transforming the single nonlocal…
The inflationary paradigm has transformed our understanding of the early universe; yet most inflationary models are considered geodesically past-incomplete, suggesting a beginning of time or a primordial Big Bang singularity. The…
In this work we study the existence of classical solutions for a class of reaction-diffusion systems with quadratic growth naturally arising in mass action chemistry when studying networks of reactions of the type $A_i+A_j…
Single-species reaction-diffusion systems on a one-dimensional lattice are considered, in them more than two neighboring sites interact. Constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution…
The present paper deals with the existence and uniqueness of global classical solutions to the continuous coagulation and nonlinear multiple fragmentation equations for large classes of unbounded coagulation, collision and breakup kernels.…