相关论文: A non-local population model of logistic type equa…
In this paper we study a toy model of the Peskin problem that captures the motion of the full Peskin problem in the normal direction and discards the tangential elastic stretching contributions. This model takes the form of a fully…
We consider a class of nonlinear Schr\"odinger equation in two space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in $L^2$)…
We consider a dispersive equation of Schr{\"o}dinger type with a non-linearity slightly larger than cubic by a logarithmic factor. This equation is supposed to be an effective model for stable two dimensional quantum droplets with LHY…
We carry out an analysis of the existence of solutions for a class of nonlinear partial differential equations of parabolic type. The equation is associated to a nonlocal initial condition, written in general form which includes, as…
Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous engineering, natural science and control problems. Yet, practically valuable results are rare in this area. This paper develops a…
This paper studies the dynamical behavior of classical solutions to a hyperbolic system of balance laws, derived from a chemotaxis model with logarithmic sensitivity, subject to time-dependent boundary conditions. It is shown that under…
We study a forager-exploiter model with generalized logistic sources in a smooth bounded domain with homogeneous Neumann boundary conditions. A new boundedness criterion is developed to prove the global existence and boundedness of the…
We establish uniform Lipschitz estimates for second-order elliptic systems in divergence form with rapidly oscillating, almost-periodic coefficients. We give interior estimates as well as estimates up to the boundary in bounded…
We prove global existence, uniqueness and $\L1$ stability of solutions to general systems of nonlocal conservation laws modeling multiclass vehicular traffic. Each class follows its own speed law and has specific effects on the other…
In our work we study non-variational, nonlinear singularly perturbed elliptic models enjoying a double degeneracy character with prescribed boundary value in a domain. In such a scenario, we establish the existence of solutions. We also…
We obtain global existence results for the Cauchy problem associated to the Schrodinger-Debye system for a class of data with infinite mass (L2-norm). A smallness condition on data is assumed. Our results include data such as…
The analysis of non-local regularisations of scalar conservation laws is an active research program. Applications of such equations are found in the modelling of physical phenomena such as traffic flow. In this paper, we propose a novel…
We consider the Cauchy problem for the nonlinear Schr\"odinger equation on $\mathbb{R}^d$, where the initial data is in $\dot{H}^1(\mathbb{R}^d)\cap L^p(\mathbb{R}^d)$. We prove local well-posedness for large ranges of $p$ and discuss some…
We prove $L^2$-maximal regularity of linear non-autonomous evolutionary Cauchy problem \begin{equation}\label{eq00}\nonumber \dot{u} (t)+A(t)u(t)=f(t) \hbox{ for }\ \hbox{a.e. t}\in [0,T],\quad u(0)=u_0, \end{equation} where the operator…
In this work, we study the pattern solutions of doubly nonlocal logistic map that include spatial kernels in both growth and competition terms. We show that this map includes as a particular case the nonlocal Fisher-Kolmogorov equation, and…
In this paper we consider a physiologically structured population model with distributed states at birth, formulated on the space of non-negative Radon measures. Using a characterisation of the pre-dual space of bounded Lipschitz functions,…
We consider the problem of determining the unknown boundary values of a solution of an elliptic equation outside a bounded open set $B$ from the knowledge of the values of this solution on a boundary of an arbitrary Lipschitz bounded domain…
The main result of the paper is a global asymptotic stability result for solutions to the Lifschitz-Slyozov-Wagner (LSW) system of equations. This extends some local asymptotic stability results of Niethammer-Vel\'{a}zquez (2006). The…
We study boundary value problems for bounded uniform domains in $\mathbb{R}^n$, $n\geq 2$, with non-Lipschitz (and possibly fractal) boundaries. We prove Poincar\'e inequalities with trace terms and uniform constants for uniform…
We study a reaction-diffusion equation with a nonlocal reaction term that models a population with variable motility. We establish a global supremum bound for solutions of the equation. We investigate the asymptotic (long-time and…