scholarly journals On an Initial Boundary Value Problem for a Class of Odd Higher Order Pseudohyperbolic Integrodifferential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Said Mesloub
Keyword(s):  
Boundary Value Problem ◽  
A Priori Estimates ◽  
Boundary Value ◽  
Nonlocal Conditions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Generalized Solution ◽  
Higher Order ◽  
Well Posedness ◽  
Initial Boundary Value

This paper is devoted to the study of the well-posedness of an initial boundary value problem for an odd higher order nonlinear pseudohyperbolic integrodifferential partial differential equation. We associate to the equationnnonlocal conditions andn+1classical conditions. Upon some a priori estimates and density arguments, we first establish the existence and uniqueness of the strongly generalized solution in a class of a certain type of Sobolev spaces for the associated linear mixed problem. On the basis of the obtained results for the linear problem, we apply an iterative process in order to establish the well-posedness of the nonlinear problem.

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 Well-posedness of bounded solutions of the non-homogeneous initial-boundary value problem for the Ostrovsky–Hunter equation

2015 ◽  
Vol 12 (02) ◽  
pp. 221-248 ◽  
Author(s):  
Giuseppe Maria Coclite ◽  
Lorenzo di Ruvo
Keyword(s):  
Boundary Value Problem ◽  
Nonlinear Evolution ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Finite Depth ◽  
Well Posedness ◽  
Rotating Fluid ◽  
Bounded Solutions ◽  
Initial Boundary Value

The Ostrovsky–Hunter equation provides a model for small-amplitude long waves in a rotating fluid of finite depth. It is a nonlinear evolution equation. Here the well-posedness of bounded solutions for a non-homogeneous initial-boundary value problem associated with this equation is studied.

An investigation of the Green–Lindsay three-dimensional model

2017 ◽  
Vol 23 (7) ◽  
pp. 987-1003 ◽  
Author(s):  
Gia Avalishvili ◽  
Mariam Avalishvili ◽  
Wolfgang H Müller
Keyword(s):  
Boundary Value Problem ◽  
Variational Formulation ◽  
A Priori Estimates ◽  
Boundary Value ◽  
Relaxation Times ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Three Dimensional Model ◽  
Initial Boundary Value

In this paper we consider the Green and Lindsay nonclassical model for inhomogeneous anisotropic thermoelastic bodies with two relaxation times, which depend on space variables. We obtain a variational formulation for the initial-boundary value problem corresponding to the Green–Lindsay model. On the basis of the variational formulation we define the spaces of vector-valued distributions corresponding to the initial-boundary value problem and by applying suitable a priori estimates we prove the existence and uniqueness of the solution, an energy equality, and the continuous dependence of the solution on given data.

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