scholarly journals Kawahara-Burgers Equation on a Strip

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
N. A. Larkin
Keyword(s):  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Burgers Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Regular Solutions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Initial Boundary Value ◽  
Channel Type

An initial-boundary value problem for the 2D Kawahara-Burgers equation posed on a channel-type strip was considered. The existence and uniqueness results for regular and weak solutions in weighted spaces as well as exponential decay of small solutions without restrictions on the width of a strip were proven both for regular solutions in an elevated norm and for weak solutions in theL2-norm.

scholarly journals The 2D Zakharov-Kuznetsov-Burgers equation on a strip

2016 ◽  
Vol 34 (1) ◽  
pp. 151-172 ◽  
Author(s):  
Nikolai Andreevitch Larkine
Keyword(s):  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Burgers Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Regular Solutions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Initial Boundary Value ◽  
Channel Type

An initial-boundary value problem for the 2D Zakharov-Kuznetsov-Burgers equation posed on a channel-type strip was considered. The existence and uniqueness results for regular and weak solutions in weighted spaces as well as exponential decay of small solutions without restrictions on the width of a strip were proven both for regular solutions in an elevated norm and for weak solutions in the $L^2$-norm.

scholarly journals Existence and Uniqueness of Weak Solutions for the Model Representing Motions of Curves Made of Elastic Materials

2021 ◽  
Vol 36 ◽  
pp. 44-56
Author(s):  
T. Aiki ◽  
◽  
C. Kosugi ◽  
Keyword(s):  
Mathematical Model ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Beam Equation ◽  
Elastic Materials ◽  
Existence Of Weak Solutions ◽  
Uniqueness And Existence ◽  
Initial Boundary Value

We consider the initial boundary value problem for the beam equation with the nonlinear strain. In our previous work this problem was proposed as a mathematical model for stretching and shrinking motions of the curve made of the elastic material on the plane. The aim of this paper is to establish uniqueness and existence of weak solutions. In particular, the uniqueness is proved by applying the approximate dual equation method.

On the convergence of difference schemes for the generalized BBM–Burgers equation

2019 ◽  
Vol 26 (3) ◽  
pp. 341-349 ◽  
Author(s):  
Givi Berikelashvili ◽  
Manana Mirianashvili
Keyword(s):  
Exact Solution ◽  
Sobolev Space ◽  
Difference Scheme ◽  
Absolute Stability ◽  
Burgers Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Algebraic Equations ◽  
The Difference ◽  
Initial Boundary Value

Abstract A three-level finite difference scheme is studied for the initial-boundary value problem of the generalized Benjamin–Bona–Mahony–Burgers equation. The obtained algebraic equations are linear with respect to the values of the desired function for each new level. The unique solvability and absolute stability of the difference scheme are shown. It is proved that the scheme is convergent with the rate of order {k-1} when the exact solution belongs to the Sobolev space {W_{2}^{k}(Q)} , {1<k\leq 3} .

scholarly journals Existence and decay of finite energy solutions for semilinear dissipative wave equations in time-dependent domains

2020 ◽  
Vol 40 (6) ◽  
pp. 725-736
Author(s):  
Mitsuhiro Nakao
Keyword(s):  
Existence And Uniqueness ◽  
Wave Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Finite Energy ◽  
Time Dependent ◽  
Energy Solution ◽  
Noncylindrical Domain ◽  
Finite Energy Solution ◽  
Initial Boundary Value

We consider the initial-boundary value problem for semilinear dissipative wave equations in noncylindrical domain \(\bigcup_{0\leq t \lt\infty} \Omega(t)\times\{t\} \subset \mathbb{R}^N\times \mathbb{R}\). We are interested in finite energy solution. We derive an exponential decay of the energy in the case \(\Omega(t)\) is bounded in \(\mathbb{R}^N\) and the estimate \[\int\limits_0^{\infty} E(t)dt \leq C(E(0),\|u(0)\|)< \infty\] in the case \(\Omega(t)\) is unbounded. Existence and uniqueness of finite energy solution are also proved.

scholarly journals On the evolution of solutions of Burgers equation on the positive quarter-plane

2019 ◽  
Vol 52 (1) ◽  
pp. 237-248
Author(s):  
Esen Hanaç
Keyword(s):  
Boundary Condition ◽  
Analytic Solution ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Condition ◽  
Quarter Plane ◽  
Initial Boundary Value ◽  
Good Agreement

AbstractIn this paper we investigate an initial-boundary value problem for the Burgers equation on the positive quarter-plane; $\matrix{ {{v_t} + v{v_x} - {v_{xx}} = 0,\,\,\,x > 0,\,\,\,t > 0,} \cr {v\left( {x,0} \right) = {u_ + },\,\,\,x > 0,} \cr {v\left( {0,t} \right) = {u_b},\,\,t > 0,} \cr }$ where x and t represent distance and time, respectively, and u+ is an initial condition, ub is a boundary condition which are constants (u+ ≠ ub). Analytic solution of above problem is solved depending on parameters (u+ and ub) then compared with numerical solutions to show there is a good agreement with each solutions.

scholarly journals Local and Global Existence of Solution for Love Type Waves with Past History

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1998
Author(s):  
Mohamed Biomy ◽  
Khaled Zennir ◽  
Ahmed Himadan
Keyword(s):  
Existence And Uniqueness ◽  
Past History ◽  
Local Existence ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Linearization Method ◽  
Weak Compactness ◽  
Existence Of Solution ◽  
Local Existence And Uniqueness ◽  
Initial Boundary Value

In this paper, we consider an initial boundary value problem for nonlinear Love equation with infinite memory. By combining the linearization method, the Faedo–Galerkin method, and the weak compactness method, the local existence and uniqueness of weak solution is proved. Using the potential well method, it is shown that the solution for a class of Love-equation exists globally under some conditions on the initial datum and kernel function.

scholarly journals On the Solutions of a Porous Medium Equation with Exponent Variable

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Huashui Zhan
Keyword(s):  
Porous Medium ◽  
Weak Solutions ◽  
Boundary Value ◽  
Porous Medium Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Medium Equation ◽  
Special Cases ◽  
The Stability ◽  
Initial Boundary Value

The paper studies the initial-boundary value problem of a porous medium equation with exponent variable. How to deal with nonlinear term with the exponent variable is the main dedication of this paper. The existence of the weak solution is proved by the monotone convergent method. Moreover, according to the different boundary value conditions, the stability of weak solutions is studied. In some special cases, the stability of weak solutions can be proved without any boundary value condition.

TWO DISCRETIZATION SCHEMES FOR A TIME-DOMAIN DISSIPATIVE ACOUSTICS PROBLEM

2006 ◽  
Vol 16 (10) ◽  
pp. 1559-1598 ◽  
Author(s):  
ALFREDO BERMÚDEZ ◽  
RODOLFO RODRÍGUEZ ◽  
DUARTE SANTAMARINA
Keyword(s):  
Time Domain ◽  
Existence And Uniqueness ◽  
Energy Equation ◽  
Time Discretization ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Temperature Fields ◽  
Displacement Fields ◽  
Discretization Schemes ◽  
Initial Boundary Value

This paper deals with a time-domain mathematical model for dissipative acoustics and is organized as follows. First, the equations of this model are written in terms of displacement and temperature fields and an energy equation is obtained. The resulting initial-boundary value problem is written in a functional framework allowing us to prove the existence and uniqueness of solution. Next, two different time-discretization schemes are proposed, and stability and error estimates are proved for both. Finally, numerical results are reported which were obtained by combining these time-schemes with Lagrangian and Raviart–Thomas finite elements for temperature and displacement fields, respectively.

Sign in / Sign up

Export Citation Format

Share Document