1,721,050 research outputs found
On Relaxation Hyperbolic Systems Violating the Shizuta-Kawashima Condition
No full textIn this paper, we start a general study on relaxation hyperbolic systems which violate the Shizuta–Kawashima coupling condition ([SK]). This investigation is motivated by the fact that this condition is in general not satisfied by various physical systems, and almost all the time in several space dimensions. First, we explore the role of entropy functionals around equilibrium solutions, which may be not constant, proposing a stability condition for such solutions. Then we find strictly dissipative entropy functions for one dimensional 2 × 2 systems which violate [SK] condition. Finally, we prove the existence of global smooth
solutions for a class of systems such that condition [SK] does not hold, but which are linearly degenerated in the non dissipative directions
A pressure model of immune response to mycobacterium tuberculosis infection in several space dimensions
No full textMycobacterium tuberculosis (Mtb) is a widely diffused infection. However, in general, the human immune system is able to contain it. In this work, we propose a mathematical model which describes the early immune response to the Mtb infection in the lungs, also including the possible evolution of the infection in the formation of a granuloma. The model is based on coupled reaction-diffusion-transport equations with chemotaxis, which take into account the interactions among bacteria, macrophages and chemoattractant. The novelty of this approach is in the modeling of the velocity field, proportional to the gradient of the pressure developed between the cells, which makes possible to deal with a full multidimensional description and efficient numerical simulations. We perform a linear stability analysis of the model and propose a robust implicit-explicit scheme to deal with long time simulations. Both in one and two-dimensions, we find that there are threshold values in the parameters space, between a contained infection and the uncontrolled bacteria growth, and the generation of granuloma-like patterns can be observed numerically
Global Smooth Solutions for a Hyperbolic Chemotaxis Model on a Network
No full textIn this paper we study a semilinear hyperbolic-parabolic system modeling biological phenomena evolving on a network composed of oriented arcs. We prove the existence of global (in time) smooth solutions to this problem. The result is obtained by using energy estimates with suitable transmission conditions at nodes
Conservation laws with discontinuous flux
No full textWe consider a hyperbolic conservation law with discontinuous flux. Such a partial differential equation arises in different applications, in particu- lar we are motivated by a model of traffic flow. We provide a new formulation in terms of Riemann Solvers. Moreover, we determine the class of Riemann Solvers which provide existence and uniqueness of the corresponding weak en- tropic solutions
Determinazione dell’Evoluzione delle Croste in Gesso mediante un Modello Matematico: Analisi Numerica e Risultati Sperimentali
No full textA rare mutation model in a spatial heterogeneous environment
Get PDFWe propose a stochastic model in evolutionary game theory where individuals (or subpopulations) can mutate changing their strategies randomly (but rarely) and explore the external environment. This environment affects the selective pressure by modifying the payoff arising from the interactions between strategies. We derive a Fokker-Planck integro-differential equation and provide Monte Carlo simulations for the Hawks vs Doves game. In particular we show that, in some cases, taking into account the external environment favors the persistence of the low-fitness strategy
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