scholarly journals A PROBLEM WITH DISPLACEMENTS IN THE BOUNDARY CONDITIONS

2017 ◽  
Vol 17 (8) ◽  
pp. 102-107
Author(s):  
E.A. Utkina
Keyword(s):  
Boundary Conditions ◽  
Unknown Function ◽  
A Priori Estimates ◽  
Hyperbolic Equations ◽  
A Priori ◽  
Fredholm Equations ◽  
Priori Estimates ◽  
Linear Hyperbolic Equations

A problem with conditions relating to the values of an unknown function on the opposite sides of a rectangular characteristiс domain D for a linear hyperbolic equations is considered. This problem is reduced to the system of Fredholm equations of the second kind. The proof of solvability is based on the a priori estimates of additional conditions on the coefficients of the equation.

scholarly journals Uniform a priori estimates for elliptic problems with impedance boundary conditions

2020 ◽  
Vol 19 (5) ◽  
pp. 2445-2471
Author(s):  
Théophile Chaumont-Frelet ◽  
◽  
Serge Nicaise ◽  
Jérôme Tomezyk ◽  
Keyword(s):  
Boundary Conditions ◽  
A Priori Estimates ◽  
A Priori ◽  
Elliptic Problems ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions ◽  
Priori Estimates

scholarly journals On the solvability of parabolic and hyperbolic problems with a boundary integral condition

2002 ◽  
Vol 31 (4) ◽  
pp. 201-213 ◽  
Author(s):  
Abdelfatah Bouziani
Keyword(s):  
A Priori Estimates ◽  
Hyperbolic Equations ◽  
A Priori ◽  
Integral Condition ◽  
Generalized Solution ◽  
Boundary Integral ◽  
Analysis Method ◽  
Hyperbolic Problems ◽  
Priori Estimates ◽  
Abstract Formulation

We prove the existence, uniqueness, and the continuous dependence of a generalized solution upon the data of certain parabolic and hyperbolic equations with a boundary integral condition. The proof uses a functional analysis method based on a priori estimates established in nonclassical function spaces, and on the density of the range of the linear operator associated to the abstract formulation of the studied problem.

scholarly journals A QUANTUM TRANSMITTING SCHRÖDINGER–POISSON SYSTEM

2004 ◽  
Vol 16 (03) ◽  
pp. 281-330 ◽  
Author(s):  
M. BARO ◽  
H.-CHR. KAISER ◽  
H. NEIDHARDT ◽  
J. REHBERG
Keyword(s):  
Boundary Conditions ◽  
Bounded Domain ◽  
Real Axis ◽  
A Priori Estimates ◽  
A Priori ◽  
Poisson System ◽  
Transparent Boundary Conditions ◽  
Bounded Interval ◽  
Zero Current ◽  
Priori Estimates

We study a stationary Schrödinger–Poisson system on a bounded interval of the real axis. The Schrödinger operator is defined on the bounded domain with transparent boundary conditions. This allows us to model a non-zero current through the boundary of the interval. We prove that the system always admits a solution and give explicit a priori estimates for the solutions.

scholarly journals An Energy Inequality and Its Applications of Nonlocal Boundary Conditions of Mixed Problem for Singular Parabolic Equations in Nonclassical Function Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Moussa Zakari Djibibe ◽  
Kokou Tcharie ◽  
N. Iossifovich Yurchuk
Keyword(s):  
Boundary Conditions ◽  
Mixed Problem ◽  
A Priori Estimates ◽  
A Priori ◽  
Energy Inequality ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Function Spaces ◽  
Priori Estimates ◽  
Singular Parabolic Equations

The aim of this paper is to establish a priori estimates of the following nonlocal boundary conditions mixed problem for parabolic equation: ∂v/∂t-(a(t)/x2)(∂/∂x)(x2∂v/∂x)+b(x,t)v=g(x,t), v(x, 0)=ψ(x), 0≤x≤ℓ, v(ℓ, t)=E(t), 0≤t≤T, ∫0ℓx3v(x,t)dx=G(t), 0≤t≤ℓ. It is important to know that a priori estimates established in nonclassical function spaces is a necessary tool to prove the uniqueness of a strong solution of the studied problems.

A PRIORI BOUNDS ON SPATIAL MOTIONS OF INCOMPRESSIBLE NONLINEARLY ELASTIC RODS

2006 ◽  
Vol 03 (03) ◽  
pp. 481-504 ◽  
Author(s):  
STUART S. ANTMAN
Keyword(s):  
Evolution Equations ◽  
A Priori Estimates ◽  
Hyperbolic Equations ◽  
A Priori ◽  
Careful Analysis ◽  
Elastic Rods ◽  
Governing Equations ◽  
Mathematical Structures ◽  
Priori Estimates ◽  
Nonlinearly Elastic

The geometrically exact quasilinear evolution equations governing the spatial motion of incompressible rods and their specializations to the hyperbolic equations governing nonlinearly elastic rods have novel mathematical structures strikingly different from those for the equations governing the motion of compressible rods. The main objectives of this paper are to formulate the governing equations, an exercise requiring the solution of a sequence of semilinear hyperbolic equations of first order, and to derive a priori estimates for certain strain variables, ensuring that they cannot reach geometrically prohibited ranges in finite time. This process exhibits a new system of physically important quasilinear equations worthy of careful analysis.

scholarly journals A priori estimates for the Fractional p-Laplacian with nonlocal Neumann boundary conditions and applications

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Dimitri Mugnai ◽  
Kanishka Perera ◽  
Edoardo Proietti Lippi
Keyword(s):  
Boundary Conditions ◽  
Morse Theory ◽  
A Priori Estimates ◽  
A Priori ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Priori Estimates ◽  
Variational Tools

<p style='text-indent:20px;'>We first prove that solutions of fractional <i>p</i>-Laplacian problems with nonlocal Neumann boundary conditions are bounded and then we apply such a result to study some resonant problems by means of variational tools and Morse theory.</p>

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