Damped wave equation in the subcritical case

We study large time asymptotics of small solutions to the Cauchy problem for the one dimensional nonlinear damped wave equation

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Nanocylinder-array structure greatly increases the soft X-ray intensity generated from femtosecond-laser-produced plasma

In order to increase the soft X-ray conversion efficiency for the femtosecond-laser-produced plasma, we adopted a nanocylinder-array structure target. Gold nanocylinder-array targets with 70–90 nm cylinder diameter and 100 nm cylinder pitch were made. A continuous smooth soft X-ray spectrum adequate for X-ray absorption spectroscopy was obtained. An around 20-fold soft X-ray (7–20 nm) fluence enhancement compared with a flat-surface gold foil target was obtained when the cylinder height was 18 μm. X-ray (>0.06 keV) pulse duration was 17 ps, which is much shorter than that obtained by using the pre-pulse technique. The X-ray pulse peak intensity was 7-fold higher than that of a gold foil target. Received: 2 May 2001 / Revised version: 1 June 2001 / Published online: 18 July 2001     

Asymptotics of solutions to the periodic problem for the nonlinear damped wave equation

We study large time asymptotic behavior of solutions to the periodic problem for the nonlinear damped wave equation

Numerical verifications of solutions for elliptic equations in nonconvex polygonal domains

Summary In this paper, methods for numerical verifications of solutions for elliptic equations in nonconvex polygonal domains are studied. In order to verify solutions using computer, it is necessary to determine some constants which appear in a priori error estimations. We propose some methods for determination of these constants. In numerical examples, calculating these constants for anL-shaped domain, we verify the solution of a nonlinear elliptic equation.     

Scattering operator for nonlinear Klein-Gordon equations in higher space dimensions

We prove the existence of the scattering operator in the neighborhood of the origin in the weighted Sobolev space Hβ,1 with for the nonlinear Klein-Gordon equation with a power nonlinearity

     

Guaranteed error bounds for finite element approximations of noncoercive elliptic problems and their applications

In this paper, we discuss with guaranteed a priori and a posteriori error estimates of finite element approximations for not necessarily coercive linear second order Dirichlet problems. Here, ‘guaranteed’ means we can get the error bounds in which all constants included are explicitly given or represented as a numerically computable form. Using the invertibility condition of concerning elliptic operator, guaranteed a priori and a posteriori error estimates are formulated. This kind of estimates plays essential and important roles in the numerical verification of solutions for nonlinear elliptic problems. Several numerical examples that confirm the actual effectiveness of the method are presented.