相关论文: The Age-Structured Chemostat with Substrate Dynami…
In this work we establish conditions which guarantee the existence of (strictly) positive steady states of a nonlinear structured population model. In our framework the steady state formulation amounts to recasting the nonlinear problem as…
We study a class of degenerate hyperbolic equations in a bounded domain whose degeneracy occurs at a boundary point. We first develop the weighted functional framework, prove well-posedness of the degenerate problem, and establish…
In this paper, we consider an age-structured mechanical model for tumor growth. This model takes into account the life-cycle of tumor cells by including an age variable. The underlying process for tumor growth is the same as classical tumor…
Structured populations are ubiquitous across the biological sciences. Mathematical models of these populations allow us to understand how individual physiological traits drive the overall dynamics in aggregate. For example, linear age- or…
In this article we are interested in the boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space. We extend the so called "backstepping method" by introducing…
We study the dynamics of a classical disordered macroscopic model completely isolated from the environment reproducing, in a classical setting, the "quantum quench" protocol. We show that, depending on the pre and post quench parameters the…
In this paper, we consider the exogenous chemotaxis system with physical mixed zero-flux and Dirichlet boundary conditions in one dimension. Since the Dirichlet boundary condition can not contribute necessary estimates for the…
This paper is concerned with the initial-boundary value problem for a nonlinear hyperbolic system of conservation laws. We study the boundary layers that may arise in approximations of entropy discontinuous solutions. We consider both the…
The random first order transition theory of the dynamics of supercooled liquids is extended to treat aging phenomena in nonequilibrium structural glasses. A reformulation of the idea of ``entropic droplets'' in terms of libraries of local…
This work is devoted to the design of boundary controls of physical systems that are described by semilinear hyperbolic balance laws. A computational framework is presented that yields sufficient conditions for a boundary control to steer…
The main purpose of this paper is the study of second-order optimality conditions for the bilinear control of a strongly degenerate parabolic equation. The equation is degenerate at the boundary of the spatial domain. The well-posedness of…
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…
The paper deals with the control and regulation by integral controllers forthe nonlinear systems governed by scalar quasi-linear hyperbolic partial differentialequations. Both the control input and the measured output are located on the…
Localized growth in driven materials is often governed by intermittent failure, yet how a material's history biases failure sites remains poorly understood. Using pause-restart experiments on chemical precipitate membranes, we quantify the…
We consider the temporal periodic solutions to general nonhomogeneous quasilinear hyperbolic equations with a kind of weak diagonal dominant structure. Under the temporal periodic boundary conditions, the existence, stability and uniqueness…
We develop theoretical equivalences between stochastic and deterministic models for populations of individual cells stratified by age. Specifically, we develop a hierarchical system of equations describing the full dynamics of an…
We discuss a class of linear control problems in a Hilbert space setting, which covers diverse systems such as hyperbolic and parabolic equations with boundary control and boundary observation even including memory terms. We introduce…
We establish a mixed observability inequality for a class of degenerate hyperbolic equations on the cylindrical domain $\Omega = \mathbb{T} \times (0,1)$ with mixed Neumann Dirichlet boundary conditions. The degeneracy acts only in the…
This paper focuses on the analysis of an optimal control problem governed by a nonsmooth quasilinear partial differential equation that models a stationary incompressible shear-thickening fluid. We start by studying the directional…
Recent biological evidence suggests the presence of a two-phase ageing process in several species. We introduce a system of two age-structured partial differential equations (PDE) representing two phases of ageing of a wild population. The…