scholarly journals Determination of an Unknown Coefficient in the Third Order Pseudoparabolic Equation with Non-Self-Adjoint Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Yashar T. Mehraliyev ◽  
Gulshan Kh. Shafiyeva
Keyword(s):  
Boundary Conditions ◽  
Classical Solution ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Unknown Coefficient ◽  
Pseudoparabolic Equation ◽  
Third Order ◽  
System Of Integral Equations ◽  
Inverse Boundary ◽  
The Third

The solvability of the inverse boundary problem with an unknown coefficient dependent on time for the third order pseudoparabolic equation with non-self-adjoint boundary conditions is investigated in the present paper. Here we have introduced the definition of the classical solution of the considered inverse boundary value problem, which is reduced to the system of integral equations by the Fourier method. At first, the existence and uniqueness of the solution of the obtaining system of integral equations is proved by the method of contraction mappings; then the existence and uniqueness of the classical solution of the stated problem is proved.

scholarly journals On Solvability of an Inverse Boundary Value Problem for Pseudo Hyperbolic Equation of the Fourth Order

2015 ◽  
Vol 7 (2) ◽  
pp. 101
Author(s):  
Yashar T. Mehraliyev ◽  
Afaq F. Huseynova
Keyword(s):  
Hyperbolic Equation ◽  
Integral Equations ◽  
Fourth Order ◽  
Existence And Uniqueness ◽  
Fourier Method ◽  
Unknown Coefficient ◽  
Classical Solutions ◽  
Equivalent Problem ◽  
Inverse Boundary ◽  
Uniqueness Of The Solution

We analyze the solvability of the inverse boundary problem with an unknown  coefficient depended on time for the pseudo hyperbolic equation of fourth order with periodic and integral conditions.The initial problem is reduced to an equivalent problem. With the help of the Fourier method, the equivalent problem is reduced to a system of integral equations. The existence and uniqueness of the solution of the integral equations is proved. The obtained solution of the integral equations is also the only solution to the equivalent problem. Basing on the equivalence of the problems, the theorem of the existence and uniqueness of the classical solutions of the original problem is proved.

scholarly journals The Regularity of the Solutions of Inverse Problems for the Pseudoparabolic Equation

2001 ◽  
Vol 14 (4) ◽  
pp. 414-424
Author(s):  
Anna Sh. Lyubanova ◽  
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Continuous Dependence ◽  
Input Data ◽  
Order Term ◽  
Unknown Coefficient ◽  
Pseudoparabolic Equation ◽  
Third Order ◽  
Additional Information ◽  
The Third

The paper discusses the regularity of the solutions to the inverse problems on finding unknown coefficients dependent on t in the pseudoparabolic equation of the third order with an additional information on the boundary. By the regularity is meant the continuous dependence of the solution on the input data of the inverse problem. The regularity of the solution is proved for two inverse problems of recovering the unknown coefficient in the second order term and the leader term of the linear pseudoparabolic equation

A Two-Dimensional Potential Flow Model of the Wave Field Generated by a Semisubmerged Body in Heaving Motion

1988 ◽  
Vol 32 (02) ◽  
pp. 83-91
Author(s):  
X. M. Wang ◽  
M. L. Spaulding
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Flow Model ◽  
Second Order ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
Potential Flow Model ◽  
Good Agreement

A two-dimensional potential flow model is formulated to predict the wave field and forces generated by a sere!submerged body in forced heaving motion. The potential flow problem is solved on a boundary fitted coordinate system that deforms in response to the motion of the free surface and the heaving body. The full nonlinear kinematic and dynamic boundary conditions are used at the free surface. The governing equations and associated boundary conditions are solved by a second-order finite-difference technique based on the modified Euler method for the time domain and a successive overrelaxation (SOR) procedure for the spatial domain. A series of sensitivity studies of grid size and resolution, time step, free surface and body grid redistribution schemes, convergence criteria, and free surface body boundary condition specification was performed to investigate the computational characteristics of the model. The model was applied to predict the forces generated by the forced oscillation of a U-shaped cylinder. Numerical model predictions are generally in good agreement with the available second-order theories for the first-order pressure and force coefficients, but clearly show that the third-order terms are larger than the second-order terms when nonlinearity becomes important in the dimensionless frequency range 1≤ Fr≤ 2. The model results are in good agreement with the available experimental data and confirm the importance of the third order terms.

scholarly journals A reaction infiltration problem: classical solutions

1997 ◽  
Vol 40 (2) ◽  
pp. 275-291 ◽  
Author(s):  
John Chadam ◽  
Xinfu Chen ◽  
Roberto Gianni ◽  
Riccardo Ricci
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Parabolic Equation ◽  
Elliptic Equation ◽  
Boundary Conditions ◽  
Classical Solution ◽  
Existence And Uniqueness ◽  
Classical Solutions ◽  
Bounded Domains ◽  
Global Classical Solution

In this paper, we consider a reaction infiltration problem consisting of a parabolic equation for the concentration, an elliptic equation for the pressure, and an ordinary differential equation for the porosity. Existence and uniqueness of a global classical solution is proved for bounded domains Ω⊂RN, under suitable boundary conditions.

scholarly journals Boundary value problem with integral conditions for a linear third-order equation

2003 ◽  
Vol 2003 (11) ◽  
pp. 553-567 ◽  
Author(s):  
M. Denche ◽  
A. Memou
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Strong Solution ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Order Equation ◽  
Integral Conditions ◽  
Third Order ◽  
Integral Boundary

We prove the existence and uniqueness of a strong solution for a linear third-order equation with integral boundary conditions. The proof uses energy inequalities and the density of the range of the generated operator.

scholarly journals Positive Solutions for Third-Order Boundary-Value Problems with the Integral Boundary Conditions and Dependence on the First-Order Derivatives

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yanping Guo ◽  
Fei Yang
Keyword(s):  
Fixed Point ◽  
Green Function ◽  
Boundary Conditions ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Third Order ◽  
Integral Boundary ◽  
First Order ◽  
The Third ◽  
Nonnegative Continuous Function

By using a fixed point theorem in a cone and the nonlocal third-order BVP's Green function, the existence of at least one positive solution for the third-order boundary-value problem with the integral boundary conditionsx′′′(t)+f(t,x(t),x′(t))=0,t∈J,x(0)=0,x′′(0)=0, andx(1)=∫01g(t)x(t)dtis considered, wherefis a nonnegative continuous function,J=[0,1], andg∈L[0,1].The emphasis here is thatfdepends on the first-order derivatives.

scholarly journals Nonlocal inverse boundary-value problem for a 2D parabolic equation with integral overdetermination condition

2020 ◽  
Vol 12 (1) ◽  
pp. 23-33
Author(s):  
E.I. Azizbayov ◽  
Y.T. Mehraliyev
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Original Problem ◽  
Boundary Value ◽  
Auxiliary Problem ◽  
Rectangular Domain ◽  
Unknown Coefficient ◽  
Inverse Boundary ◽  
Inverse Boundary Value Problem

This article studies a nonlocal inverse boundary-value problem for a two-dimensional second-order parabolic equation in a rectangular domain. The purpose of the article is to determine the unknown coefficient and the solution of the considered problem. To investigate the solvability of the inverse problem, we transform the original problem into some auxiliary problem with trivial boundary conditions. Using the contraction mappings principle, existence and uniqueness of the solution of an equivalent problem are proved. Further, using the equivalency, the existence and uniqueness theorem of the classical solution of the original problem is obtained.

scholarly journals Existence Theory for Nonlinear Third-Order Ordinary Differential Equations with Nonlocal Multi-Point and Multi-Strip Boundary Conditions

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 281 ◽  
Author(s):  
Ahmed Alsaedi ◽  
Mona Alsulami ◽  
Hari Srivastava ◽  
Bashir Ahmad ◽  
Sotiris Ntouyas
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Existence Theory ◽  
Ulam Stability ◽  
Point Boundary ◽  
Arbitrary Domain ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
The Third ◽  
Nonlocal Nonlinear

We investigate the solvability and Ulam stability for a nonlocal nonlinear third-order integro-multi-point boundary value problem on an arbitrary domain. The nonlinearity in the third-order ordinary differential equation involves the unknown function together with its first- and second-order derivatives. Our main results rely on the modern tools of functional analysis and are well illustrated with the aid of examples. An analogue problem involving non-separated integro-multi-point boundary conditions is also discussed.

Sign in / Sign up

Export Citation Format

Share Document