Displaying similar documents to “Transport Equation Reduction for a Mathematical Model in Plant Growth”

Variational Reduction for the Transport Equation in a Multiple Branching Plants Growth Model

S. Boujena, A. Chiboub, J. Pousin (2010)

Mathematical Modelling of Natural Phenomena

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Plant growth depends essentially on nutrients coming from the roots and metabolites produced by the plant. Appearance of new branches is determined by concentrations of certain plant hormones. The most important of them are Auxin and Cytokinin. Auxin is produced in the growing, Cytokinin in either roots or in growing parts. Many dynamical models of this phenomena have been studied in [1]. In [5], the authors deal with one branch model....

Mathematical analysis and numerical simulation of a Reynolds-Koiter model for the elastohydrodynamic journal-bearing device

Iñigo Arregui, J. Jesús Cendán, Carlos Vázquez (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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The aim of this work is to deduce the existence of solution of a coupled problem arising in elastohydrodynamic lubrication. The lubricant pressure and concentration are modelled by Reynolds equation, jointly with the free-boundary Elrod-Adams model in order to take into account cavitation phenomena. The bearing deformation is solution of Koiter model for thin shells. The existence of solution to the variational problem presents some difficulties: the coupled character of the equations,...

Conical differentiability for bone remodeling contact rod models

Isabel N. Figueiredo, Carlos F. Leal, Cecília S. Pinto (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We prove the conical differentiability of the solution to a bone remodeling contact rod model, for given data (applied loads and rigid obstacle), with respect to small perturbations of the cross section of the rod. The proof is based on the special structure of the model, composed of a variational inequality coupled with an ordinary differential equation with respect to time. This structure enables the verification of the two following fundamental results: the polyhedricity of a modified...

Exterior problem of the Darwin model and its numerical computation

Lung-an Ying, Fengyan Li (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper, we study the exterior boundary value problems of the Darwin model to the Maxwell's equations. The variational formulation is established and the existence and uniqueness is proved. We use the infinite element method to solve the problem, only a small amount of computational work is needed. Numerical examples are given as well as a proof of convergence.

On the analysis of boundary value problems in nonsmooth domains

Gilles Frémiot, Werner Horn, Antoine Laurain, Murali Rao, Jan Sokołowski

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Problems involving cracks are of particular importance in structural mechanics, and gave rise to many interesting mathematical techniques to treat them. The difficulties stem from the singularities of domains, which yield lower regularity of solutions. Of particular interest are techniques which allow us to identify cracks and defects from the mechanical properties. Long before advent of mathematical modeling in structural mechanics, defects were identified by the fact that they changed...

Guaranteed and computable bounds of the limit load for variational problems with linear growth energy functionals

Jaroslav Haslinger, Sergey Repin, Stanislav Sysala (2016)

Applications of Mathematics

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The paper is concerned with guaranteed and computable bounds of the limit (or safety) load, which is one of the most important quantitative characteristics of mathematical models associated with linear growth functionals. We suggest a new method for getting such bounds and illustrate its performance. First, the main ideas are demonstrated with the paradigm of a simple variational problem with a linear growth functional defined on a set of scalar valued functions. Then, the method is...

Existence and uniqueness results for non-Newtonian fluids of the Oldroyd type in unbounded domains

Rodolfo Salvi (2005)

Banach Center Publications

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In the paper [13], we give the full system of equations modelling the motion of a fluid/viscoelastic solid system, and obtain a differential model similar to the so-called Oldroyd model for a viscoelastic fluid. Moreover, existence results in bounded domains are obtained. In this paper we extend the results in [13] to unbounded domains. The unique solvability of the system of equations is established locally in time and globally in time with so-called smallness restrictions. Moreover,...

Elasticity of A + XB[X] when A ⊂ B is a minimal extension of integral domains

Ahmed Ayache, Hanen Monceur (2011)

Colloquium Mathematicae

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We investigate the elasticity of atomic domains of the form ℜ = A + XB[X], where X is an indeterminate, A is a local domain that is not a field, and A ⊂ B is a minimal extension of integral domains. We provide the exact value of the elasticity of ℜ in all cases depending the position of the maximal ideals of B. Then we investigate when such domains are half-factorial domains.

A note on Costara's paper

Armen Edigarian (2004)

Annales Polonici Mathematici

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We show that the symmetrized bidisc 𝔾₂ = {(λ₁+λ₂,λ₁λ₂):|λ₁|,|λ₂| < 1} ⊂ ℂ² cannot be exhausted by domains biholomorphic to convex domains.