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Displaying 121 – 140 of 290

On the behaviour of generalized solutions to genuinely nonlinear first order equations for small and large values of time.

Yu. G. Rykov (1993)

Revista Matemática de la Universidad Complutense de Madrid

The paper deals with the asymptotic behavior of generalized solutions to nonlinear first order equations. With the aid of explicit variational representation one studies the decrease of solutions for a large time. And for the small time an asymptotic of the perturbation?s front is calculated.

On the best observation of wave and Schrödinger equations in quantum ergodic billiards

Yannick Privat, Emmanuel Trélat, Enrique Zuazua (2012)

Journées Équations aux dérivées partielles

This paper is a proceedings version of the ongoing work [20], and has been the object of the talk of the second author at Journées EDP in 2012.In this work we investigate optimal observability properties for wave and Schrödinger equations considered in a bounded open set $Ω \subset ℝ^{n}$ , with Dirichlet boundary conditions. The observation is done on a subset $ω$ of Lebesgue measure $| ω | = L | Ω |$ , where $L \in (0, 1)$ is fixed. We denote by $𝒰_{L}$ the class of all possible such subsets. Let $T > 0$ . We consider first the benchmark problem of maximizing...

On the blowing up of solutions to nonlinear wave equations in two space dimensions.

M.A. Rammaha (1988)

Journal für die reine und angewandte Mathematik

On the boundary value problem in a dihedral angle for normally hyperbolic systems of first order.

Jokhadze, O. (1998)

Georgian Mathematical Journal

On the Cauchy problem for hyperbolic functional-differential equations

Adrian Karpowicz, Henryk Leszczyński (2015)

Annales Polonici Mathematici

We consider the Cauchy problem for a nonlocal wave equation in one dimension. We study the existence of solutions by means of bicharacteristics. The existence and uniqueness is obtained in $W_{l o c}^{1, \infty}$ topology. The existence theorem is proved in a subset generated by certain continuity conditions for the derivatives.

On the Cauchy problem for linear hyperbolic functional-differential equations

Alexander Lomtatidze, Jiří Šremr (2012)

Czechoslovak Mathematical Journal

We study the question of the existence, uniqueness, and continuous dependence on parameters of the Carathéodory solutions to the Cauchy problem for linear partial functional-differential equations of hyperbolic type. A theorem on the Fredholm alternative is also proved. The results obtained are new even in the case of equations without argument deviations, because we do not suppose absolute continuity of the function the Cauchy problem is prescribed on, which is rather usual assumption in the existing...

On The Cauchy Problem for Non Effectively Hyperbolic Operators, The Ivrii-Petkov-Hörmander Condition and the Gevrey Well Posedness

Nishitani, Tatsuo (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 35L15, Secondary 35L30.In this paper we prove that for non effectively hyperbolic operators with smooth double characteristics with the Hamilton map exhibiting a Jordan block of size 4 on the double characteristic manifold the Cauchy problem is well posed in the Gevrey 6 class if the strict Ivrii-Petkov-Hörmander condition is satisfied.

On the Cauchy problem for the equations of ideal compressible MHD fluids with radiation

Christian Rohde, Wojciech M. Zajączkowski (2003)

Applications of Mathematics

We consider a system of balance laws describing the motion of an ionized compressible fluid interacting with magnetic fields and radiation effects. The local-in-time existence of a unique smooth solution for the Cauchy problem is proven. The proof follows from the method of successive approximations.

On the characteristic initial value problem for nonlinear symmetric hyperbolic systems, including Einstein equations [Book]

Aurore Cabet, Piotr T. Chruściel, Roger Tagne Wafo (2016)

On the Chebyshev penalty method for parabolic and hyperbolic equations

Lucia Dettori, Baolin Yang (1996)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

On the computation of roll waves

Shi Jin, Yong Jung Kim (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The phenomenon of roll waves occurs in a uniform open-channel flow down an incline, when the Froude number is above two. The goal of this paper is to analyze the behavior of numerical approximations to a model roll wave equation $u_{t} + u u_{x} = u, u (x, 0) = u_{0} (x),$ which arises as a weakly nonlinear approximation of the shallow water equations. The main difficulty associated with the numerical approximation of this problem is its linear instability. Numerical round-off error can easily overtake the numerical solution and yields false...

On the Computation of Roll Waves

Shi Jin, Yong Jung Kim (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The phenomenon of roll waves occurs in a uniform open-channel flow down an incline, when the Froude number is above two. The goal of this paper is to analyze the behavior of numerical approximations to a model roll wave equation ut + uux = u,u(x,0) = u0(x), which arises as a weakly nonlinear approximation of the shallow water equations. The main difficulty associated with the numerical approximation of this problem is its linear instability. Numerical round-off error can easily overtake the...

On the connection between some Riemann-solver free approaches to the approximation of multi-dimensional systems of hyperbolic conservation laws

Tim Kröger, Sebastian Noelle, Susanne Zimmermann (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, we present some interesting connections between a number of Riemann-solver free approaches to the numerical solution of multi-dimensional systems of conservation laws. As a main part, we present a new and elementary derivation of Fey’s Method of Transport (MoT) (respectively the second author’s ICE version of the scheme) and the state decompositions which form the basis of it. The only tools that we use are quadrature rules applied to the moment integral used in the gas kinetic derivation...

On the connection between some Riemann-solver free approaches to the approximation of multi-dimensional systems of hyperbolic conservation laws

Tim Kröger, Sebastian Noelle, Susanne Zimmermann (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we present some interesting connections between a number of Riemann-solver free approaches to the numerical solution of multi-dimensional systems of conservation laws. As a main part, we present a new and elementary derivation of Fey's Method of Transport (MoT) (respectively the second author's ICE version of the scheme) and the state decompositions which form the basis of it. The only tools that we use are quadrature rules applied to the moment integral used in the...

On the controllability of the 1-D isentropic Euler equation

Olivier Glass (2007)

Journal of the European Mathematical Society

We study the controllability problem for the one-dimensional Euler isentropic system, both in Eulerian and Lagrangian coordinates, by means of boundary controls, in the context of weak entropy solutions. We give a sufficient condition on the initial and final states under which the first one can be steered to the latter.

On the controllability under constraints on the control for hyperbolic equations.

Dehman, Belhassen, Omrane, Abdennebi (2010)

Applied Mathematics E-Notes [electronic only]

On the Convergence Rate Estimates for Finite Difference Schemes Approximating Homogeneous Initial-boundary Value Problem for Hyperbolic Equation

Vladimir Jovanović (1996)

Publications de l'Institut Mathématique

Currently displaying 121 – 140 of 290

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Displaying 121 – 140 of 290

On the behaviour of generalized solutions to genuinely nonlinear first order equations for small and large values of time.

On the best observation of wave and Schrödinger equations in quantum ergodic billiards

On the blowing up of solutions to nonlinear wave equations in two space dimensions.

On the boundary value problem in a dihedral angle for normally hyperbolic systems of first order.

On the Cauchy problem for hyperbolic functional-differential equations

On the Cauchy problem for linear hyperbolic functional-differential equations

On The Cauchy Problem for Non Effectively Hyperbolic Operators, The Ivrii-Petkov-Hörmander Condition and the Gevrey Well Posedness

On the Cauchy problem for the equations of ideal compressible MHD fluids with radiation

On the characteristic initial value problem for nonlinear symmetric hyperbolic systems, including Einstein equations [Book]

On the Chebyshev penalty method for parabolic and hyperbolic equations

On the computation of roll waves

On the Computation of Roll Waves

On the connection between some Riemann-solver free approaches to the approximation of multi-dimensional systems of hyperbolic conservation laws

On the connection between some Riemann-solver free approaches to the approximation of multi-dimensional systems of hyperbolic conservation laws

On the controllability of the 1-D isentropic Euler equation

On the controllability under constraints on the control for hyperbolic equations.

On the Convergence Rate Estimates for Finite Difference Schemes Approximating Homogeneous Initial-boundary Value Problem for Hyperbolic Equation

On the correct formulation of a multidimensional problem for strictly hyperbolic equations of higher order.

On the correctness of the Dirichlet problem in a characteristic rectangle for fourth order linear hyperbolic equations.

On the coupled system of nonlinear wave equations with different propagation speeds

Currently displaying 121 – 140 of 290