Study of the dissipativity, global attractor and exponential attractor for a hyperbolic relaxation of the Caginalp phase-field system with singular nonlinear terms

2020 ◽  
pp. 1-28
Author(s):  
Urbain Cyriaque Mavoungou ◽  
Narcisse Batangouna ◽  
Franck Davhys Reval Langa ◽  
Daniel Moukoko ◽  
Macaire Batchi
Keyword(s):  
Boundary Condition ◽  
Global Attractor ◽  
Phase Field ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Exponential Attractor ◽  
Field System ◽  
Phase Field System

In this paper, we study of the dissipativity, global attractor and exponential attractor for a hyperbolic relaxation of the Caginalp phase-field system with singular nonlinear terms, with initial and homogenous Dirichlet boundary condition.

scholarly journals Global attractor for a parabolic-hyperbolic Penrose-Fife phase field system

2006 ◽  
Vol 15 (4) ◽  
pp. 1193-1214
Author(s):  
Elisabetta Rocca ◽  
◽  
Giulio Schimperna ◽  
Keyword(s):  
Global Attractor ◽  
Phase Field ◽  
Field System ◽  
Phase Field System

scholarly journals Existence and uniqueness of solution for Cahn-Hilliard hyperbolic phase field system with Dirichlet boundary conditions and polynomial potential

2018 ◽  
Vol 7 (1) ◽  
pp. 10
Author(s):  
A. J. Bissouesse ◽  
Daniel Moukoko ◽  
Franck Langa ◽  
Macaire Batchi
Keyword(s):  
Boundary Conditions ◽  
Phase Field ◽  
Dirichlet Boundary ◽  
Initial Conditions ◽  
Dirichlet Boundary Conditions ◽  
Uniqueness Of Solution ◽  
Polynomial Potential ◽  
Field System ◽  
Phase Field System ◽  
Homogeneous Dirichlet Boundary Conditions

Our aim in this article is to study the existence and the uniqueness of solution for Cahn-Hilliard hyperbolic phase-field system, with initial conditions, homogeneous Dirichlet boundary conditions, polynomial potential in a bounded and smooth domain.

scholarly journals Existence and Uniqueness of Solution for Caginalp Hyperbolic Phase- Field System with a Polynomial Potential

2018 ◽  
Vol 10 (1) ◽  
pp. 124
Author(s):  
Franck Davhys Reval Langa ◽  
Daniel Moukoko ◽  
Dieudonn Ampini ◽  
Fidle Moukamba
Keyword(s):  
Bounded Domain ◽  
Phase Field ◽  
Existence And Uniqueness ◽  
Dirichlet Boundary ◽  
Initial Conditions ◽  
Uniqueness Of Solution ◽  
Uniqueness Of Solutions ◽  
Polynomial Potential ◽  
Field System ◽  
Phase Field System

We prove the existence and the uniqueness of solutions for Caginalp hyperbolic phase-field system with initial conditions, Dirichlet boundary homogeneous conditions and a regular potential of order $2p-1$, in bounded domain.

scholarly journals FINITE-DIMENSIONAL GLOBAL ATTRACTOR FOR A NONLOCAL PHASE-FIELD SYSTEM

2012 ◽  
Author(s):  
Maurizio Grasselli
Keyword(s):  
Global Attractor ◽  
Phase Field ◽  
Energy Balance Equation ◽  
Absorbing Set ◽  
Field System ◽  
Finite Dimensional ◽  
Long Range Interactions ◽  
Bounded Absorbing Set ◽  
Singular Configuration ◽  
Phase Field System

We analyze a phase-field system where the energy balance equation is linearly coupled with a nonlinear and nonlocal ODE for the order parameter . The latter equation is characterized by a space convolution term which models long-range interactions and a singular configuration potential that forces to take values in the interval (􀀀1; 1). We prove that the corresponding dynamical system is dissipative, i.e., it has a bounded absorbing set in a suitable phase space. Then we establish the existence of a finite-dimensional global attractor.

scholarly journals On some classes of generalized Schrödinger equations

2020 ◽  
Vol 10 (1) ◽  
pp. 522-533
Author(s):  
Amanda S. S. Correa Leão ◽  
Joelma Morbach ◽  
Andrelino V. Santos ◽  
João R. Santos Júnior
Keyword(s):  
Boundary Condition ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Laplacian Operator ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Stationary Problems

Abstract Some classes of generalized Schrödinger stationary problems are studied. Under appropriated conditions is proved the existence of at least 1 + $\begin{array}{} \sum_{i=2}^{m} \end{array}$ dim Vλi pairs of nontrivial solutions if a parameter involved in the equation is large enough, where Vλi denotes the eigenspace associated to the i-th eigenvalue λi of laplacian operator with homogeneous Dirichlet boundary condition.

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