Sufficient conditions for the blowup of a solution to the Boussinesq equation subject to a nonlinear Neumann boundary condition

2008 ◽  
Vol 48 (11) ◽  
pp. 2077-2080 ◽  
Author(s):  
M. O. Korpusov ◽  
A. G. Sveshnikov
Keyword(s):  
Boundary Condition ◽  
Neumann Boundary Condition ◽  
Boussinesq Equation ◽  
Sufficient Conditions ◽  
Neumann Boundary

scholarly journals Pointwise observation of the state given by complex time lag parabolic system

2017 ◽  
Vol 27 (1) ◽  
pp. 77-89
Author(s):  
Adam Kowalewski
Keyword(s):  
Boundary Condition ◽  
Parabolic System ◽  
Neumann Boundary Condition ◽  
Optimization Problems ◽  
Time Lag ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
The State ◽  
Constant Time ◽  
Time Lags

AbstractVarious optimization problems for linear parabolic systems with multiple constant time lags are considered. In this paper, we consider an optimal distributed control problem for a linear complex parabolic system in which different multiple constant time lags appear both in the state equation and in the Neumann boundary condition. Sufficient conditions for the existence of a unique solution of the parabolic time lag equation with the Neumann boundary condition are proved. The time horizon T is fixed. Making use of the Lions scheme [13], necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functional with pointwise observation of the state and constrained control are derived. The example of application is also provided.

Stability and Instability of the Wave Equation Solutions in a Pulsating Domain

1998 ◽  
Vol 10 (07) ◽  
pp. 925-962 ◽  
Author(s):  
J. Dittrich ◽  
P. Duclos ◽  
N. Gonzalez
Keyword(s):  
Boundary Condition ◽  
Neumann Boundary Condition ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
D’Alembert Equation ◽  
Stability And Instability ◽  
Unlimited Growth ◽  
Neumann Type ◽  
Finite Space ◽  
Space Interval

The behavior of energy is studied for the real scalar field satisfying d'Alembert equation in a finite space interval 0<x<a(t); the endpoint a(t) is assumed to move slower than the light and periodically in most parts of the paper. The boundary conditions are of Dirichlet and Neumann type. We give sufficient conditions for the unlimited growth, the boundedness and the periodicity of the energy E. The case of unbounded energy without infinite limit (0< lim inf t→+∞E(t) < lim sup t→+∞E(t)=+∞) is also possible. For the Neumann boundary condition, E may decay to zero as the time tends to infinity. If a is periodic, the solution is determined by a homeomorphism [Formula: see text] of the circle related to a. The behavior of E depends essentially on the number theoretical characteristics of the rotation number of [Formula: see text].

scholarly journals Pointwise observation of the state given by parabolic system with boundary condition involving multiple time delays

2016 ◽  
Vol 26 (2) ◽  
pp. 189-197 ◽  
Author(s):  
Adam Kowalewski
Keyword(s):  
Boundary Condition ◽  
Parabolic System ◽  
Neumann Boundary Condition ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
The State ◽  
Constant Time ◽  
Multiple Time ◽  
Multiple Time Delays

Abstract Various optimization problems for linear parabolic systems with multiple constant time delays are considered. In this paper, we consider an optimal distributed control problem for a linear parabolic system in which multiple constant time delays appear in the Neumann boundary condition. Sufficient conditions for the existence of a unique solution of the parabolic equation with the Neumann boundary condition involving multiple time delays are proved. The time horizon T is fixed. Making use of the Lions scheme [13], necessary and sufficient conditions of optimality for the Neumann problem with the quadratic cost function with pointwise observation of the state and constrained control are derived.

Inverse spectral problem of an anharmonic oscillator on a half-axis with the Neumann boundary condition

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Agil K. Khanmamedov ◽  
Nigar F. Gafarova
Keyword(s):  
Boundary Condition ◽  
Neumann Boundary Condition ◽  
Inverse Spectral Problem ◽  
Anharmonic Oscillator ◽  
Neumann Boundary ◽  
Effective Algorithm ◽  
Inverse Spectral Problems ◽  
Main Equation ◽  
Inverse Spectral ◽  
Half Axis

AbstractAn anharmonic oscillator {T(q)=-\frac{d^{2}}{dx^{2}}+x^{2}+q(x)} on the half-axis {0\leq x<\infty} with the Neumann boundary condition is considered. By means of transformation operators, the direct and inverse spectral problems are studied. We obtain the main integral equations of the inverse problem and prove that the main equation is uniquely solvable. An effective algorithm for reconstruction of perturbed potential is indicated.

scholarly journals Blow-Up Analysis for a Quasilinear Parabolic Equation with Inner Absorption and Nonlinear Neumann Boundary Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong Bo Fang ◽  
Yan Chai
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Neumann Boundary Condition ◽  
Blow Up ◽  
Quasilinear Parabolic Equation ◽  
Neumann Boundary ◽  
Initial Boundary ◽  
Blow Up Analysis ◽  
Inner Absorption ◽  
Quasilinear Parabolic

We investigate an initial-boundary value problem for a quasilinear parabolic equation with inner absorption and nonlinear Neumann boundary condition. We establish, respectively, the conditions on nonlinearity to guarantee thatu(x,t)exists globally or blows up at some finite timet*. Moreover, an upper bound fort*is derived. Under somewhat more restrictive conditions, a lower bound fort*is also obtained.

An efficient MILU preconditioning for solving the 2D Poisson equation with Neumann boundary condition

2018 ◽  
Vol 356 ◽  
pp. 115-126 ◽  
Author(s):  
Yesom Park ◽  
Jeongho Kim ◽  
Jinwook Jung ◽  
Euntaek Lee ◽  
Chohong Min
Keyword(s):  
Boundary Condition ◽  
Poisson Equation ◽  
Neumann Boundary Condition ◽  
Neumann Boundary
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