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The aim of this paper is to analyze a model for chemotaxis based on a local sensing mechanism instead of the gradient sensing mechanism used in the celebrated minimal Keller-Segel model. The model we study has the same entropy as the…
This paper is concerned with a parabolic-elliptic chemotaxis model with density-suppressed motility and general logistic source in an $n$-dimensional smooth bounded domain with Neumann boundary conditions. Under the minimal conditions for…
The aim of this article is to study a Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects, degenerate mobility and where only one of the species does separate from the others. We define a notion of weak solution…
Hyperbolic systems in one dimensional space are frequently used in modeling of many physical systems. In our recent works, we introduced time independent feedbacks leading to the finite stabilization for the optimal time of homogeneous…
A retrovirus dynamic model is proposed. We pay attention to the case when viral pathogenicity is low and the infected cells are able to reproduce. Using Lyapunov function method we study stability properties of an inner equilibrium of the…
A spectral-fractional Cahn-Hilliard cross-diffusion system, which describes the pre-patterning of lymphatic vessel morphology in collagen gels, is studied. The model consists of two higher-order quasilinear parabolic equations and describes…
We exhibit a large class of Lyapunov functionals for nonlinear drift-diffusion equations with non-homogeneous Dirichlet boundary conditions. These are generalizations of large deviation functionals for underlying stochastic many-particle…
We introduce static and dynamic correlation functions for the spatial densities of Lyapunov vector fluctuations. They enable us to show, for the first time, the existence of hydrodynamic Lyapunov modes in chaotic many-particle systems with…
The aim of this paper is to construct invariant regions of a generalized m-component reaction-diffusion system with a tri-diagonal Toeplitz matrix of diffusion coefficients and prove the global existence of solutions using Lyapunov…
New sufficient conditions for the characterization of dwell-times for linear impulsive systems are proposed and shown to coincide with continuous decrease conditions of a certain class of looped-functionals, a recently introduced type of…
We study the weak solvability of a system of coupled Allen-Cahn-like equations resembling cross-diffusion which is arising as a model for the consolidation of saturated porous media. Besides using energy like estimates, we cast the special…
This paper is devoted to investigate the pattern formation of a volume-filling chemotaxis model with logistic cell growth. We first apply the local stability analysis to establish sufficient conditions of destabilization for uniform…
We study a complex non-newtonian fluid that models the flow of nematic liquid crystals. The fluid is described by a system that couples a forced Navier-Stokes system with a parabolic-type system. We prove the existence of global weak…
The global-in-time existence of weak solutions to a degenerate Cahn-Hilliard cross-diffusion system with singular potential in a bounded domain with no-flux boundary conditions is proved. The model consists of two coupled parabolic…
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 macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
We propose and analyze a one-dimensional multi-species cross-diffusion system with non-zero-flux boundary conditions on a moving domain, motivated by the mod- eling of a Physical Vapor Deposition process. Using the boundedness by entropy…
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:…
A variety of enhanced statistical and numerical methods are now routinely used to extract comprehensible and relevant thermodynamic information from the vast amount of complex, high-dimensional data obtained from intensive molecular…
The impact of turbulent mixing on the droplet size distribution is studied deep inside a warm ice-free cloud. A simplified cloud mixing model was implemented therefore which summarizes the balance equations of water vapor mixing ratio and…