scholarly journals $\mathcal {E}$-well posedness of mixed initial-boundary value problem with constant coefficients in a quarter space, II

1980 ◽  
Vol 56 (7) ◽  
pp. 318-320
Author(s):  
Yoshihiro Shibata
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Well Posedness ◽  
Constant Coefficients ◽  
Quarter Space ◽  
Initial Boundary Value

scholarly journals Well-posedness of bounded solutions of the non-homogeneous initial-boundary value problem for the Ostrovsky–Hunter equation

2015 ◽  
Vol 12 (02) ◽  
pp. 221-248 ◽  
Author(s):  
Giuseppe Maria Coclite ◽  
Lorenzo di Ruvo
Keyword(s):  
Boundary Value Problem ◽  
Nonlinear Evolution ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Finite Depth ◽  
Well Posedness ◽  
Rotating Fluid ◽  
Bounded Solutions ◽  
Initial Boundary Value

The Ostrovsky–Hunter equation provides a model for small-amplitude long waves in a rotating fluid of finite depth. It is a nonlinear evolution equation. Here the well-posedness of bounded solutions for a non-homogeneous initial-boundary value problem associated with this equation is studied.

scholarly journals WELL-POSEDNESS FOR THE MASSIVE WAVE EQUATION ON ASYMPTOTICALLY ANTI-DE SITTER SPACETIMES

2012 ◽  
Vol 09 (02) ◽  
pp. 239-261 ◽  
Author(s):  
GUSTAV HOLZEGEL
Keyword(s):  
Wave Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Energy Class ◽  
Well Posedness ◽  
De Sitter ◽  
Initial Boundary Value

In this paper, we prove a well-posedness theorem for the massive wave equation (with the mass satisfying the Breitenlohner–Freedman bound) on asymptotically anti-de Sitter spaces. The solution is constructed as a limit of solutions to an initial boundary value problem with boundary at a finite location in spacetime by finally pushing the boundary out to infinity. The solution obtained is unique within the energy class (but non-unique if the decay at infinity is weakened).

scholarly journals AN INTRODUCTION TO WELL-POSEDNESS AND FREE-EVOLUTION

2013 ◽  
Vol 28 (22n23) ◽  
pp. 1340015 ◽  
Author(s):  
DAVID HILDITCH
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Initial Value Problem ◽  
Boundary Value ◽  
Fourier Method ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Well Posedness ◽  
Initial Value ◽  
Initial Boundary Value

These lecture notes accompany two classes given at the NRHEP2 school. In the first lecture I introduce the basic concepts used for analyzing well-posedness, that is the existence of a unique solution depending continuously on given data, of evolution partial differential equations. I show how strong hyperbolicity guarantees well-posedness of the initial value problem. Symmetric hyperbolic systems are shown to render the initial boundary value problem well-posed with maximally dissipative boundary conditions. I discuss the Laplace–Fourier method for analyzing the initial boundary value problem. Finally, I state how these notions extend to systems that are first-order in time and second-order in space. In the second lecture I discuss the effect that the gauge freedom of electromagnetism has on the PDE status of the initial value problem. I focus on gauge choices, strong-hyperbolicity and the construction of constraint preserving boundary conditions. I show that strongly hyperbolic pure gauges can be used to build strongly hyperbolic formulations. I examine which of these formulations is additionally symmetric hyperbolic and finally demonstrate that the system can be made boundary stable.

scholarly journals Formulation and analysis of a parabolic transmission problem on disjoint intervals

2012 ◽  
Vol 91 (105) ◽  
pp. 111-123 ◽  
Author(s):  
Bosko Jovanovic ◽  
Lubin Vulkov
Keyword(s):  
Boundary Value Problem ◽  
Weak Solutions ◽  
Parabolic Equations ◽  
Input Data ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Well Posedness ◽  
One Dimensional ◽  
Initial Boundary Value

We investigate an initial-boundary-value problem for one dimensional parabolic equations in disjoint intervals. Under some natural assumptions on the input data we proved the well-posedness of the problem. Nonnegativity and energy stability of its weak solutions are also studied.

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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