scholarly journals An initial-boundary value problem for quasi-linear parabolic systems of higher order

1974 ◽  
Vol 30 (2) ◽  
pp. 145-164
Author(s):  
Vladimír Ďurikovič
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Parabolic Systems ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Higher Order ◽  
Initial Boundary Value

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 Higher Order Wave Equation with Logarithmic Source Term

2017 ◽  
Author(s):  
Sh. Hajrulla ◽  
L. Bezati ◽  
F. Hoxha
Keyword(s):  
Wave Equation ◽  
Boundary Value Problem ◽  
Source Term ◽  
Boundary Value ◽  
Initial Boundary ◽  
Global Weak Solution ◽  
Initial Boundary Value Problem ◽  
Logarithmic Sobolev Inequality ◽  
Higher Order ◽  
Initial Boundary Value

In this paper we study the initial boundary value problem for logarithmic Higher Order Wave equation. Introducing the Logarithmic Sobolev inequality and using the combination of Galerkin method, we consider the theorem of existence of a global weak solution to problem for the initial boundary value problem of the logarithmic wave equation. By constructing an appropriate Lyapunov function, we obtain the decay estimates of energy for logarithmic Higher Order Wave equation. The proof of the main theorem is given.

scholarly journals On Initial-Boundary Value Problem on Semiaxis for Generalized Kawahara Equation

2019 ◽  
Vol 65 (4) ◽  
pp. 683-699
Author(s):  
A. V. Faminskii ◽  
E. V. Martynov
Keyword(s):  
Boundary Value Problem ◽  
Global Solution ◽  
Existence And Uniqueness ◽  
Large Time ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Higher Order ◽  
Kawahara Equation ◽  
Initial Boundary Value

In this paper, we consider initial-boundary value problem on semiaxis for generalized Kawahara equation with higher-order nonlinearity. We obtain the result on existence and uniqueness of the global solution. Also, if the equation contains the absorbing term vanishing at infinity, we prove that the solution decays at large time values.

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.

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