scholarly journals A Wave Equation Associated with Mixed Nonhomogeneous Conditions: The Compactness and Connectivity of Weak Solution Set

2007 ◽  
Vol 2007 ◽  
pp. 1-17
Author(s):  
Nguyen Thanh Long ◽  
Le Thi Phuong Ngoc
Keyword(s):  
Wave Equation ◽  
Weak Solution ◽  
Boundary Value Problem ◽  
Weak Solutions ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Linear Wave ◽  
Linear Wave Equation ◽  
Initial Boundary Value

The purpose of this paper is to show that the set of weak solutions of the initial-boundary value problem for the linear wave equation is nonempty, connected, and compact.

Weak solutions to the initial-boundary value problem for the shearing of non-homogeneous thermoviscoplastic materials

1989 ◽  
Vol 113 (3-4) ◽  
pp. 257-265 ◽  
Author(s):  
Nicolas Charalambakis ◽  
François Murat
Keyword(s):  
Weak Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Weak Solutions ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Temperature Dependent ◽  
Initial Boundary Value

SynopsisWe prove the existence of a weak solution for the system of partial differential equations describing the shearing of stratified thermoviscoplastic materials with temperature-dependent non-homogeneous viscosity.

scholarly journals Initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Liming Xiao ◽  
Mingkun Li
Keyword(s):  
Weak Solution ◽  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Higher Order ◽  
Evolution Problem ◽  
Positive Energy ◽  
Initial Boundary Value

AbstractIn this paper, we study the initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations which do not have positive energy and come from the soil mechanics, the heat conduction, and the nonlinear optics. By the mountain pass theorem we first prove the existence of nonzero weak solution to the static problem, which is the important basis of evolution problem, then based on the method of potential well we prove the existence of global weak solution to the evolution problem.

scholarly journals Application of Initial Boundary Value Problem on Logarithmic Wave Equation in Dynamics

2018 ◽  
Author(s):  
Shkelqim Hajrulla ◽  
Leonard Bezati ◽  
Fatmir Hoxha
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Boundary Value Problem ◽  
Sobolev Inequality ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Logarithmic Sobolev Inequality ◽  
Initial Boundary Value ◽  
The Galerkin Method

We introduce a class of logarithmic wave equation. We study the global existence of week solution for this class of equation. We deal with the initial boundary value problem of this class. Using the Galerkin method and the Gross logarithmic Sobolev inequality we establish the main theorem of existence of week solution for this class of equation arising from Q-Ball Dynamic in particular.

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