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Modelling of Plant Growth with Apical or Basal Meristem

N. Bessonov, F. Crauste, V. Volpert (2011)

Mathematical Modelling of Natural Phenomena

Plant growth occurs due to cell proliferation in the meristem. We model the case of apical meristem specific for branch growth and the case of basal meristem specific for bulbous plants and grass. In the case of apical growth, our model allows us to describe the variety of plant forms and lifetimes, endogenous rhythms and apical domination. In the case of basal growth, the spatial structure, which corresponds to the appearance of leaves, results...

Multiple existence and stability of steady-states for a prey-predator system with cross-diffusion

Kousuke Kuto, Yoshio Yamada (2004)

Banach Center Publications

This article discusses a prey-predator system with cross-diffusion. We obtain multiple positive steady-state solutions of this system. More precisely, we prove that the set of positive steady-states possibly contains an S or ⊃-shaped branch with respect to a bifurcation parameter in the large cross-diffusion case. Next we give some criteria on the stability of these positive steady-states. Furthermore, we find the Hopf bifurcation point on the steady-state solution branch in a certain case. Our...

New existence and stability results for partial fractional differential inclusions with multiple delay

Saïd Abbas, Wafaa A. Albarakati, Mouffak Benchohra, Mohamed Abdalla Darwish, Eman M. Hilal (2015)

Annales Polonici Mathematici

We discuss the existence of solutions and Ulam's type stability concepts for a class of partial functional fractional differential inclusions with noninstantaneous impulses and a nonconvex valued right hand side in Banach spaces. An example is provided to illustrate our results.

Nonlinear boundary value problems describing mobile carrier transport in semiconductor devices

E. Z. Borevich, V. M. Chistyakov (2001)

Applications of Mathematics

The present paper describes mobile carrier transport in semiconductor devices with constant densities of ionized impurities. For this purpose we use one-dimensional partial differential equations. The work gives the proofs of global existence of solutions of systems of such kind, their bifurcations and their stability under the corresponding assumptions.

Numerical analysis of modular regularization methods for the BDF2 time discretization of the Navier-Stokes equations

William Layton, Nathaniel Mays, Monika Neda, Catalin Trenchea (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider an uncoupled, modular regularization algorithm for approximation of the Navier-Stokes equations. The method is: Step 1.1: Advance the NSE one time step, Step 1.1: Regularize to obtain the approximation at the new time level. Previous analysis of this approach has been for specific time stepping methods in Step 1.1 and simple stabilizations in Step 1.1. In this report we extend the mathematical support for uncoupled, modular stabilization to (i) the more complex and better performing...

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