Abstract We study the two-dimensional stochastic nonlinear heat equation (SNLH) and damped wave (SdNLW) with an exponential nonlinearity $$\lambda \beta e^{\beta u }$$ ? ? e u , forced by additive space-time white...

We present an exact solution of the equations for orbit determination of a two body system in a hyperbolic or parabolic motion. In solving this problem, we extend the method employed by Asada, Akasaka and Kasai (AAK) for a binary system in an elliptic orbit. The solutions applicable to each of elliptic, hyperbolic and parabolic ∗Email: [email protected]

In this note we announce dispersive estimates for Fourier integrals with parameter-dependent phase functions in terms of geometric quantities of associated families of Fresnel surfaces. The results are based on a multidimensional van der Corput lemma due to the first author. Applications to dispersive estimates for hyperbolic systems and scalar higher order hyperbolic equations are also discussed.