相关论文: Analysis of a one-dimensional forager-exploiter mo…
In this paper we study the zero-flux chemotaxis-system \begin{equation*} \begin{cases} u_{ t}=\nabla \cdot ((u+1)^{m-1} \nabla u-(u+1)^\alpha \chi(v)\nabla v) + ku-\mu u^2 & x\in \Omega, t>0, \\ v_{t} = \Delta v-vu & x\in \Omega, t>0,\\…
Well-posedness and uniform-in-time boundedness of classical solutions are investigated for a three-component parabolic system which describes the dynamics of a population of cells interacting with a chemoattractant and a nutrient. The…
This paper deals with the problem of global solvability and boundedness of classical solutions to a fully parabolic chemotaxis system with singular sensitivity in any dimensional setting. In particular, We show that the system…
This series of papers is concerned with the global solvability, boundedness, regularity, and uniqueness of weak solutions to the following parabolic-parabolic chemotaxis system with a logistic source and chemical consumption:…
An initial-boundary value problem for the 1D self-adjoint parabolic equation on the half-axis is solved. We study a broad family of two-level finite-difference schemes with two parameters related to averagings both in time and space.…
This paper is Part II of a series on global existence and asymptotic behavior of positive solutions to \begin{equation*} \begin{cases} \displaystyle u_t=\Delta u-\chi_0\nabla\cdot\left(\frac{u^m}{(1+v)^\beta}\nabla…
We provide sufficient and almost optimal conditions for global existence of classical solutions in parabolic H\"older spaces to quasilinear one-dimensional parabolic problems with dynamical boundary conditions.
In this paper, the fully parabolic Keller-Segel system \begin{equation} \left\{ \begin{array}{llc} u_t=\Delta u-\nabla\cdot(u\nabla v), &(x,t)\in \Omega\times (0,T),\\ v_t=\Delta v-v+u, &(x,t)\in\Omega\times (0,T),\\ \end{array} \right.…
The current paper considers the boundedness of solutions to the following quasilinear Keller-Segel model (with logistic source) $$\left\{\begin{array}{ll} u_t = \nabla\cdot(D(u)\nabla u)-\chi\nabla\cdot(u\nabla v)+\mu (u-u^2),\quad x\in…
This paper deals with a semilinear parabolic system with free boundary in one space dimension. We suppose that unknown functions $u$ and $v$ undergo nonlinear reactions $u^q$ and $v^p$, and exist initially in a interval $\{0\leq x\leq…
Multi-species reaction-diffusion systems, with nearest-neighbor interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time…
We introduce the parafermionic truncated Wigner approximation ($p$TWA), a semiclassical phase-space framework for simulating the nonequilibrium dynamics of lattice systems with fractional exchange statistics. The method extends truncated…
Assuming a non-gravitational interaction amongst the dark fluids of our universe namely, the dark matter and dark energy, we study a specific interaction model in the background of a spatially flat Friedmann-Lema\^itre-Robertson-Walker…
In this paper we investigate a free boundary problem for the diffusive Leslie-Gower prey-predator model with double free boundaries in one space dimension. This system models the expanding of an invasive or new predator species in which the…
We establish Schauder-type estimates for linear parabolic systems driven by variable-coefficient nonlocal pseudo-differential operators of order $s>0$. These estimates are formulated in critical time-weighted H\"older/Besov-type spaces and…
The paper focuses on positive solutions to a coupled system of parabolic equations with nonlocal initial conditions. Such equations arise as steady-state equations in an age-structured predator-prey model with diffusion. By using global…
We consider the stability problem for a unitary N+1 fermionic model, i.e., a system of $N$ identical fermions interacting via zero-range interactions with a different particle, in the case of infinite two-body scattering length. We present…
Gravitational and electrostatic interactions are fundamental examples of systems with long-range interactions. Equilibrium properties of simple models with long-range interactions are well understood and exhibit exotic behaviors : negative…
Mathematical modelling and numerical simulations of interaction populations are crucial topics in systems biology. The interactions of ecological models may occur among individuals of the same species or individuals of different species.…
This paper deals with the quasilinear fully parabolic attraction-repulsion chemotaxis system \begin{align*} u_t=\nabla \cdot (D(u)\nabla u) -\nabla \cdot (G(u)\chi(v)\nabla v) +\nabla\cdot(H(u)\xi(w)\nabla w), \quad v_t=d_1\Delta v+\alpha…