Let $\Omega\subset\mathbb R^2$ be a bounded domain, $\gamma\in C^{3,\alpha}(\partial\Omega;\mathbb R^3)$ ($0 <\alpha <1$) and $H>0$. Let ${h_{\gamma}}$ be the harmonic extension of $\gamma$ in $\Omega$. We show that if $a_0\in\Omega$ is a regular point of ${h_{\gamma}}$ and a nondegenerate critical point of $K(\cdot,\Omega)$ introduced in part I of this paper [3], then for small $H$, there exists a large solution ${\overline{u}_H}$ to the $H$-system $$\Delta u=2Hu_{x_1}\wedge u_{x_2}\quad\text{in $\Omega$}, \qquad u=\gamma\quad \text{on $\partial\Omega$.}$$ Moreover, ${\overline{u}_H}$ blows up (in the sense of part I) at exactly one point $a_0$ as $H\to 0$.

This paper is devoted to the existence of global solutions of the \newline Kirchhoff-Carrier equation $$u_{tt}-M\bigl(t,\int_{\Omega}\left|\nabla u\right|^2dx\bigr)\Delta u=0$$ subject to nonlinear boundary dissipation. Assuming that $M(t,\lambda )\geq m_0>0$, we prove the existence and uniqueness of regular solutions without any smallness on the initial data. Moreover, uniform decay rates are obtained by assuming a nonlinear feedback acting on the boundary.

The frequency and the direction of propagation of an oscillatory wave train may be read on its oscillatory spectrum. Many works in geometrical optics allow the study of at most countable oscillatory spectra. In these works, the number of directions of propagation is therefore at most countable, while many physical effects would require a continuous infinity of directions of propagation. The goal of this paper is to make the nonlinear geometrical optics for wave trains with such a continuous oscillatory spectrum. This requires the introduction of new spaces, which are Wiener algebras associated to spaces of vector-valued measures with bounded total variation. We also make qualitative studies on the properties of wave trains with continuous oscillatory spectrum, and on the incidence of the nonlinearity on such oscillations. We finally suggest an application of the results of this paper to the study of both the spontaneous and the stimulated Raman scatterings.