EXISTENCE AND UNIQUENESS OF GLOBAL WEAK SOLUTION FOR A CLASS OF PARABOLIC TYPE EQUATIONS ASSOCIATED WITH MAXWELL’S SYSTEM

2017 ◽  
Vol 17 (4) ◽  
pp. 301-320
Author(s):  
Junichi Aramaki
Keyword(s):  
Weak Solution ◽  
Existence And Uniqueness ◽  
Parabolic Type ◽  
Global Weak Solution ◽  
Maxwell’S System

scholarly journals Qualitative analysis of solutions for a parabolic type Kirchhoff equation with logarithmic nonlinearity

2021 ◽  
Vol 4 (2) ◽  
pp. 1-10
Author(s):  
Erhan Pişkin ◽  
◽  
Tuğrul Cömert ◽  
Keyword(s):  
Weak Solution ◽  
Boundary Value Problem ◽  
Blow Up ◽  
Parabolic Type ◽  
Initial Boundary ◽  
Global Weak Solution ◽  
Initial Boundary Value Problem ◽  
Kirchhoff Equation ◽  
Potential Wells ◽  
Initial Boundary Value

In this work, we investigate the initial boundary-value problem for a parabolic type Kirchhoff equation with logarithmic nonlinearity. We get the existence of global weak solution, by the potential wells method and energy method. Also, we get results of the decay and finite time blow up of the weak solutions.

scholarly journals On the 2D Ericksen–Leslie equations with anisotropic energy and external forces

2021 ◽  
Author(s):  
Zdzislaw Brzeźniak ◽  
Gabriel Deugoué ◽  
Paul André Razafimandimby
Keyword(s):  
Weak Solution ◽  
Initial Data ◽  
Existence And Uniqueness ◽  
Global Weak Solution ◽  
Energy Modeling ◽  
External Control ◽  
Global Weak Solutions ◽  
External Data ◽  
Anisotropic Energy ◽  
External Forces

AbstractIn this paper we consider the 2D Ericksen–Leslie equations which describe the hydrodynamics of nematic liquid crystal with external body forces and anisotropic energy modeling the energy of applied external control such as magnetic or electric field. Under general assumptions on the initial data, the external data and the anisotropic energy, we prove the existence and uniqueness of global weak solutions with finitely many singular times. If the initial data and the external forces are sufficiently small, then we establish that the global weak solution does not have any singular times and is regular as long as the data are regular.

scholarly journals Optimal control of a viscous generalized θ-type dispersive equation with weak dissipation

2020 ◽  
Vol 18 (1) ◽  
pp. 1302-1316
Author(s):  
Guobing Fan ◽  
Zhifeng Yang
Keyword(s):  
Boundary Condition ◽  
Optimal Control ◽  
Weak Solution ◽  
Existence And Uniqueness ◽  
Optimal Solution ◽  
Dispersive Equation ◽  
Weak Dissipation ◽  
Formula Type

Abstract In this paper, we investigate the problem for optimal control of a viscous generalized \theta -type dispersive equation (VG \theta -type DE) with weak dissipation. First, we prove the existence and uniqueness of weak solution to the equation. Then, we present the optimal control of a VG \theta -type DE with weak dissipation under boundary condition and prove the existence of optimal solution to the problem.

A piezoelectric contact problem with slip dependent friction and damage

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Abderrezak Kasri
Keyword(s):  
Weak Solution ◽  
Contact Problem ◽  
Dry Friction ◽  
Existence And Uniqueness ◽  
Variational Formulation ◽  
Normal Compliance ◽  
Electrically Conductive ◽  
Coulomb’S Law ◽  
Electrical Condition ◽  
Coulomb's Law

Abstract The aim of this paper is to study a quasistatic contact problem between an electro-elastic viscoplastic body with damage and an electrically conductive foundation. The contact is modelled with an electrical condition, normal compliance and the associated version of Coulomb’s law of dry friction in which slip dependent friction is included. We derive a variational formulation for the model and, under a smallness assumption, we prove the existence and uniqueness of a weak solution.

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