scholarly journals Μερικές διαφορικές εξισώσεις και προβλήματα της επιστήμης των υλικών

2014 ◽  
Author(s):  
Ευτυχία Αργυροπούλου
Keyword(s):  
Hilbert Space ◽  
Main Part ◽  
Semigroup Theory ◽  
Divergence Form ◽  
Elliptic Type ◽  
Well Posedness ◽  
Initial Value ◽  
Time Harmonic ◽  
Periodic Unfolding Method ◽  
Unfolding Method

The main objective of this thesis is the homogenization of partial dierentialequations (mainly Maxwell'As equations) describing electromagneticphenomena in complex media. In particular, we study the homogenization ofMaxwell'As equations focusing on the periodic unfolding method in complexmedia under Drude-Born-Fedorov type, local in time, constitutive relations.Firstly, we formulate Maxwell'A s problem as an evolution initial value(Cauchy) problem in a Hilbert space supplemented with the constitutiverelations of a bianisotropic medium (the most general linear medium in electromagnetics).Further, we analyze the notion of homogenization and weapply it as examples to equations of elliptic type in divergence form and toMaxwell'As system in bianisotropic media.We present also the method of periodic unfolding in the case of an ellipticpartial dierential equation and in the main part of this work we considerthe problem of the well-posedness of the time-dependent Maxwell'As equationsin a Drude-Born-Fedorov type environment considering the elds to beelements of an appropriate Hilbert space. In order to prove the existence anduniqueness we apply the Faedo-Galerkin method and for the continuous dependencefrom the initial data we use semigroup theory for operators. Therest of the main part of the thesis deals with the homogenization of theconsidered problem, using the periodic unfolding method.In the last chapter, we examine the time-harmonic Maxwell problem ina bianisotropic cavity, which we study by transforming it to an eigenvalueproblem.

scholarly journals ENERGY CRITICAL NLS IN TWO SPACE DIMENSIONS

2009 ◽  
Vol 06 (03) ◽  
pp. 549-575 ◽  
Author(s):  
J. COLLIANDER ◽  
S. IBRAHIM ◽  
M. MAJDOUB ◽  
N. MASMOUDI
Keyword(s):  
Schrödinger Equation ◽  
Initial Value Problem ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Energy Space ◽  
Well Posedness ◽  
Initial Value ◽  
Exponential Nonlinearity ◽  
Supercritical Case ◽  
Two Space Dimensions

We investigate the initial value problem for a defocusing nonlinear Schrödinger equation with exponential nonlinearity [Formula: see text] We identify subcritical, critical, and supercritical regimes in the energy space. We establish global well-posedness in the subcritical and critical regimes. Well-posedness fails to hold in the supercritical case.

Well-Posedness of the Gnedenko System with Multiple Vacations

2012 ◽  
Vol 522 ◽  
pp. 902-909
Author(s):  
Bilikiz Yunus ◽  
Abdukerim Haji
Keyword(s):  
Semigroup Theory ◽  
Linear Operators ◽  
Well Posedness ◽  
Multiple Vacations ◽  
Dynamic Solution ◽  
Multiple Vacation ◽  
Gnedenko System

We investigate the solution of the Gnedenko system with multiple vacation of a repairman. By using-semigroup theory of linear operators, we prove well-posedness and the existence of the unique positive dynamic solution of the system.

The Periodic Unfolding Method

2018 ◽  
Author(s):  
Doina Cioranescu ◽  
Alain Damlamian ◽  
Georges Griso
Keyword(s):  
Periodic Unfolding Method ◽  
Unfolding Method

scholarly journals On well-posedness of time-harmonic problems in an unbounded strip for a thin plate model

2019 ◽  
Vol 17 (6) ◽  
pp. 1487-1529 ◽  
Author(s):  
Laurent Bourgeois ◽  
Lucas Chesnel ◽  
Sonia Fliss
Keyword(s):  
Thin Plate ◽  
Well Posedness ◽  
Plate Model ◽  
Time Harmonic

Well Posedness

2012 ◽  
Author(s):  
G. F. Roach ◽  
I. G. Stratis ◽  
A. N. Yannacopoulos
Keyword(s):  
Variational Formulation ◽  
Eigenvalue Problems ◽  
Dimensional Space ◽  
Well Posedness ◽  
Finite Dimensional Space ◽  
Chiral Media ◽  
Exterior Problems ◽  
Finite Dimensional ◽  
Time Harmonic ◽  
Interior Domain

This chapter presents rigorous mathematical results concerning the solvability and well posedness of time-harmonic problems for complex electromagnetic media, with a special emphasis on chiral media. It also presents some results concerning eigenvalue problems in cavities filled with complex electromagnetic materials. The chapter also studies the behaviour of the interior domain problem for a chiral medium in the limit of low chirality. Next, it presents some comments related to the well posedness and solvability of exterior problems. Finally, using an appropriate finite-dimensional space and the variational formulation of the discretised version of the original boundary value problem, this chapter obtains numerical methods for the solution of the Maxwell equations for chiral media.

scholarly journals Hyperbolic Maxwell variational inequalities of the second kind

2020 ◽  
Vol 26 ◽  
pp. 34 ◽  
Author(s):  
Irwin Yousept
Keyword(s):  
Variational Inequalities ◽  
Existence Result ◽  
Semigroup Theory ◽  
Regularity Property ◽  
Well Posedness ◽  
Test Functions ◽  
Local Boundedness ◽  
Subdifferential Calculus ◽  
Faraday’S Law ◽  
Yosida Regularization

We analyze a class of hyperbolic Maxwell variational inequalities of the second kind. By means of a local boundedness assumption on the subdifferential of the underlying nonlinearity, we prove a well-posedness result, where the main tools for the proof are the semigroup theory for Maxwell’s equations, the Yosida regularization and the subdifferential calculus. The second part of the paper focuses on a more general case omitting the local boundedness assumption. In this case, taking into account more regular initial data and test functions, we are able to prove a weaker existence result through the use of the minimal section operator associated with the Nemytskii operator of the governing subdifferential. Eventually, we transfer the developed well-posedness results to the case involving Faraday’s law, which in particular allows us to improve the regularity property of the electric field in the weak existence result.

scholarly journals An age-dependent population equation with diffusion and delayed birth process

2005 ◽  
Vol 2005 (20) ◽  
pp. 3273-3289 ◽  
Author(s):  
G. Fragnelli
Keyword(s):  
Asymptotic Behavior ◽  
Semigroup Theory ◽  
New Age ◽  
Well Posedness ◽  
Birth Process ◽  
Age Dependent ◽  
Population Equation

We propose a new age-dependent population equation which takes into account not only a delay in the birth process, but also other events that may take place during the time between conception and birth. Using semigroup theory, we discuss the well posedness and the asymptotic behavior of the solution.

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