28 citations · 28 across the 4 of their papers we have counts for
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On the wave-like energy estimates of Klein-Gordon type equations with time dependent potential
Kazunori Goto, Fumihiko Hirosawa
We consider the conditions for the time dependent potential in which the energy of the Cauchy problem of Klein-Gordon type equation asymptotically behaves like the energy of the wa…
On the energy estimates of semi-discrete wave equations with time dependent propagation speed
Fumihiko Hirosawa
Discretization is a fundamental step in numerical analysis for the problems described by differential equations, and the difference between the continuous model and discrete model…
A class of non-analytic functions for the global solvability of Kirchhoff equation
Fumihiko Hirosawa
We consider the global solvability to the Cauchy problem of Kirchhoff equation with generalized classes of Manfrin's class. Manfrin's class is a subclass of Sobolev space, but we s…
Generalised energy conservation law for the wave equations with variable propagation speed
Fumihiko Hirosawa, Jens Wirth
We investigate the long time behaviour of the -energy of solutions to wave equations with variable speed. The novelty of the approach is the combination of estimates for highe…