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Global existence for a nuclear fluid in one dimension: the T > 0 case

Bernard Ducomet (2002)

Applications of Mathematics

We consider a simplified one-dimensional thermal model of nuclear matter, described by a system of Navier-Stokes-Poisson type, with a non monotone equation of state due to an effective nuclear interaction. We prove the existence of globally defined (large) solutions of the corresponding free boundary problem, with an exterior pressure P which is not required to be positive, provided sufficient thermal dissipation is present. We give also a partial description of the asymptotic behaviour of the system,...

Global existence of weak solutions to the Fried-Gurtin model of phase transitions

Zenon Kosowski (2007)

Applicationes Mathematicae

We prove the existence of global in time weak solutions to a three-dimensional system of equations arising in a simple version of the Fried-Gurtin model for the isothermal phase transition in solids. In this model the phase is characterized by an order parameter. The problem considered here has the form of a coupled system of three-dimensional elasticity and parabolic equations. The system is studied with the help of the Faedo-Galerkin method using energy estimates.

Global in time solvability of the initial boundary value problem for some nonlinear dissipative evolution equations

Yoshihiro Shibata (1993)

Commentationes Mathematicae Universitatis Carolinae

The global in time solvability of the one-dimensional nonlinear equations of thermoelasticity, equations of viscoelasticity and nonlinear wave equations in several space dimensions with some boundary dissipation is discussed. The blow up of the solutions which might be possible even for small data is excluded by allowing for a certain dissipative mechanism.

Global synchronization of chaotic Lur’e systems via replacing variables control

Xiaofeng Wu, Yi Zhao, Muhong Wang (2008)

Kybernetika

Finding sufficient criteria for synchronization of master-slave chaotic systems by replacing variables control has been an open problem in the field of chaos control. This paper presents some recent works on the subject, with emphasis on chaos synchronization of both identical and parametrically mismatched Lur’e systems by replacing variables control. The synchronization schemes are formally constructed and two classes of sufficient criteria for global synchronization, linear matrix inequality criterion...

Global well-posedness and blow up for the nonlinear fractional beam equations

Shouquan Ma, Guixiang Xu (2010)

Applicationes Mathematicae

We establish the Strichartz estimates for the linear fractional beam equations in Besov spaces. Using these estimates, we obtain global well-posedness for the subcritical and critical defocusing fractional beam equations. Of course, we need to assume small initial data for the critical case. In addition, by the convexity method, we show that blow up occurs for the focusing fractional beam equations with negative energy.

Godunov method for nonconservative hyperbolic systems

María Luz Muñoz-Ruiz, Carlos Parés (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is concerned with the numerical approximation of Cauchy problems for one-dimensional nonconservative hyperbolic systems. The theory developed by Dal Maso et al. [J. Math. Pures Appl.74 (1995) 483–548] is used in order to define the weak solutions of the system: an interpretation of the nonconservative products as Borel measures is given, based on the choice of a family of paths drawn in the phase space. Even if the family of paths can be chosen arbitrarily, it is natural to require this...

Gradient theory for plasticity via homogenization of discrete dislocations

Adriana Garroni, Giovanni Leoni, Marcello Ponsiglione (2010)

Journal of the European Mathematical Society

We deduce a macroscopic strain gradient theory for plasticity from a model of discrete dislocations. We restrict our analysis to the case of a cylindrical symmetry for the crystal under study, so that the mathematical formulation will involve a two-dimensional variational problem. The dislocations are introduced as point topological defects of the strain fields, for which we compute the elastic energy stored outside the so-called core region. We show that the Γ -limit of this energy (suitably rescaled),...

Ground states in complex bodies

Paolo Maria Mariano, Giuseppe Modica (2009)

ESAIM: Control, Optimisation and Calculus of Variations

A unified framework for analyzing the existence of ground states in wide classes of elastic complex bodies is presented here. The approach makes use of classical semicontinuity results, Sobolev mappings and cartesian currents. Weak diffeomorphisms are used to represent macroscopic deformations. Sobolev maps and cartesian currents describe the inner substructure of the material elements. Balance equations for irregular minimizers are derived. A contribution to the debate about the role of the balance...

Ground states in complex bodies

Paolo Maria Mariano, Giuseppe Modica (2008)

ESAIM: Control, Optimisation and Calculus of Variations

A unified framework for analyzing the existence of ground states in wide classes of elastic complex bodies is presented here. The approach makes use of classical semicontinuity results, Sobolev mappings and Cartesian currents. Weak diffeomorphisms are used to represent macroscopic deformations. Sobolev maps and Cartesian currents describe the inner substructure of the material elements. Balance equations for irregular minimizers are derived. A contribution to the debate about the role of the balance...

Group synchronization of diffusively coupled harmonic oscillators

Liyun Zhao, Jun Liu, Lan Xiang, Jin Zhou (2016)

Kybernetika

This paper considers group synchronization issue of diffusively directed coupled harmonic oscillators for two cases with nonidentical and identical agent dynamics. For the case of coupled nonidentical harmonic oscillators with positive coupling, it is demonstrated that distributed group synchronization can always be achieved under two kinds of network structures, i. e., the strongly connected graph and the acyclic partition topology with a directed spanning tree. It is interesting to find that the...

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

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 extended to...

Guided waves in a fluid layer on an elastic irregular bottom.

Andrés Fraguela Collar (1996)

Publicacions Matemàtiques

In this paper one considers the linearized problem to determine the movement of an ideal heavy fluid contained in an unbounded container withelastic walls. As initial data one knows the movement of both the bottom and the free surface of the fluid and also the strength of certain perturbation, strong enough to take the bottom out of its rest state.One important point to be considered regards the influence of the bottom’s geometry on the propagation of superficial waves. This problem has been already...

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