All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 34 Next

Displaying 661 – 680 of 2227

Showing per page

Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics

Mária Lukáčová-Medviďová, Jitka Saibertová (2006)

Applications of Mathematics

In this paper we present recent results for the bicharacteristic based finite volume schemes, the so-called finite volume evolution Galerkin (FVEG) schemes. These methods were proposed to solve multi-dimensional hyperbolic conservation laws. They combine the usually conflicting design objectives of using the conservation form and following the characteristics, or bicharacteristics. This is realized by combining the finite volume formulation with approximate evolution operators, which use bicharacteristics...

Finite-volume solvers for a multilayer Saint-Venant system

Emmanuel Audusse, Marie-Odile Bristeau (2007)

International Journal of Applied Mathematics and Computer Science

We consider the numerical investigation of two hyperbolic shallow water models. We focus on the treatment of the hyperbolic part. We first recall some efficient finite volume solvers for the classical Saint-Venant system. Then we study their extensions to a new multilayer Saint-Venant system. Finally, we use a kinetic solver to perform some numerical tests which prove that the 2D multilayer Saint-Venant system is a relevant alternative to D hydrostatic Navier-Stokes equations.

Focusing of a pulse with arbitrary phase shift for a nonlinear wave equation

Rémi Carles, David Lannes (2003)

Bulletin de la Société Mathématique de France

We consider a system of two linear conservative wave equations, with a nonlinear coupling, in space dimension three. Spherical pulse like initial data cause focusing at the origin in the limit of short wavelength. Because the equations are conservative, the caustic crossing is not trivial, and we analyze it for particular initial data. It turns out that the phase shift between the incoming wave (before the focus) and the outgoing wave (past the focus) behaves like ln ε , where ε stands for the wavelength....

Focusing of spherical nonlinear pulses in R1+3. II. Nonlinear caustic.

Rémi Carles, Jeffrey Rauch (2004)

Revista Matemática Iberoamericana

We study spherical pulse like families of solutions to semilinear wave equattions in space time of dimension 1+3 as the pulses focus at a point and emerge outgoing. We emphasize the scales for which the incoming and outgoing waves behave linearly but the nonlinearity has a strong effect at the focus. The focus crossing is described by a scattering operator for the semilinear equation, which broadens the pulses. The relative errors in our approximate solutions are small in the L∞ norm.

Forced periodic vibrations of an elastic system with elastico-plastic damping

Pavel Krejčí (1988)

Aplikace matematiky

We prove the existence and find necessary and sufficient conditions for the uniqueness of the time-periodic solution to the equations u t t - Δ x u ± F ( u ) = g ( x , t ) for an arbitrary (sufficiently smooth) periodic right-hand side g , where Δ x denotes the Laplace operator with respect to x ∈ Ω ⊂ R N , N ≥ 1 , and F is the Ishlinskii hysteresis operator. For N = 2 this equation describes e.g. the vibrations of an elastic membrane in an elastico-plastic medium.

Formation of Singularities for Weakly Non-Linear N×N Hyperbolic Systems

Boiti, Chiara, Manfrin, Renato (2001)

Serdica Mathematical Journal

We present some results on the formation of singularities for C^1 - solutions of the quasi-linear N × N strictly hyperbolic system Ut + A(U )Ux = 0 in [0, +∞) × Rx . Under certain weak non-linearity conditions (weaker than genuine non-linearity), we prove that the first order derivative of the solution blows-up in finite time.

Forms, functional calculus, cosine functions and perturbation

Wolfgang Arendt, Charles J. K. Batty (2007)

Banach Center Publications

In this article we describe properties of unbounded operators related to evolutionary problems. It is a survey article which also contains several new results. For instance we give a characterization of cosine functions in terms of mild well-posedness of the Cauchy problem of order 2, and we show that the property of having a bounded H ∞ -calculus is stable under rank-1 perturbations whereas the property of being associated with a closed form and the property of generating a cosine function are not....

Currently displaying 661 – 680 of 2227