Kiyoshi Mochizuki

On Small Data Scattering for Some Nonlinear Wave Equations

Abstract We study nonlinear wave equations of the form e τ 2 w-δw+m 2 w+f(w)=0 in Euclidean space. Here m≥0 and f(w) represents power nonlinearities, the sine-Gordon nonlinearity and a cubic convolution nonlinearity. Under suitable restrictions on the nonlinearity, the scattering operator is proved to be defined on a dense domain of a neighborhood of 0 in the energy space.

One-dimensional two-phase porous flow equations

AbstractWe study initial-boundary value problems for one-dimensional two-phase porous flow equations

Radiation conditions and spectral theory for 2-body Schrödinger operators with “oscillating” long-range potentials, II, -Spectral representation-

\left\{ \begin{array}{l} V_x = 0, V = - k(x, s)p_x - a(x, s) \\ m(x)s_t = \left\{ {r(x, s)s_x + b(x, s) + Vl(s)} \right\}_x . \\ \end{array} \right.

Radiation conditions and spectral theory for 2-body Schrödinger operators with “oscillating” long-range potentials I, the principle of limiting absorption

The existence and asymptotic behavior of weak solutions are treated, with suitable coefficients and data. The proof is based on regularization and elementary energy inequalities.