Related papers: The Generic Sudden Singularity in Brans-Dicke Theo…
We study steady axisymmetric water waves with general vorticity and swirl, subject to the influence of surface tension. This can be formulated as an elliptic free boundary problem in terms of Stokes' stream function. A change of variables…
Based on the asymptotic analysis of ordinary differential equations, we classify all spherically symmetric self-similar solutions to the Einstein equations which are asymptotically Friedmann at large distances and contain a perfect fluid…
In this paper, we consider the Cauchy problem for pressureless gases in two space dimensions with generic smooth initial data (density and velocity). These equations give rise to singular curves, where the mass has positive density…
We studied spherically symmetric solutions in scalar-torsion gravity theories in which a scalar field is coupled to torsion with a derivative coupling. We obtained the general field equations from which we extracted a decoupled master…
We consider the Cauchy problem for the wave equation in a general class of spherically symmetric black hole geometries. Under certain mild conditions on the far-field decay and the singularity, we show that there is a unique globally smooth…
A symmetry of Brans-Dicke gravity in (electro-)vacuo or in the presence of conformally invariant matter is presented and used as a solution-generating technique starting from a known solution as a seed. This novel technique is applied to…
The presence and evolution of apparent horizons in a two-parameter family of spherically symmetric, time-dependent solutions of Brans-Dicke gravity are analyzed. These solutions were introduced to model space- and time-varying gravitational…
Higher dimensional, static, cylindrically symmetric vacuum solutions with and without a cosmological constant in the Brans-Dicke theory are presented. We show that, for a negative cosmological constant and for specific values of the…
We study a $q-$analog of a singularly perturbed Cauchy problem with irregular singularity in the complex domain which generalizes a previous result by S. Malek in \cite{malek}. First, we construct solutions defined in open $q-$spirals to…
We study the Cauchy problem for a nonlinear damped wave equation. Under suitable assumptions for the nonlinearity and the initial data, we obtain the global solution which satisfies weighted $L^1$ and $L^\infty$ estimates. Furthermore, we…
An asymptotic small parameter expansion of a single Cauchy problem is constructed for a singularly perturbed system of hyperbolic equations describing vibrations of two rigidly connected strings. Equations (such as generalized Korteweg-de…
Hele-Shaw flow at vanishing surface tension is ill-defined. In finite time, the flow develops cusp-like singularities. We show that the ill-defined problem admits a weak {\it dispersive} solution when singularities give rise to a graph of…
The singularity structure and the corresponding asymptotic behavior of a 3-brane coupled to a scalar field or to a perfect fluid in a five-dimensional bulk is analyzed in full generality using the method of asymptotic splittings. In the…
We study the Cauchy problem for the surface quasi-geostrophic (SQG) equations in a two-dimensional bounded domain with the homogeneous Dirichlet boundary condition. We establish the unique existence of strong solutions in the critical Besov…
We derive exact Friedmann--Robertson--Walker cosmological solutions in general scalar--tensor gravity theories, including Brans--Dicke gravity, for stiff matter or radiation. These correspond to the long or short wavelength modes…
We consider the Cauchy problem for the equations of pressureless gases in two space dimensions. For a generic set of smooth initial data (density and velocity), it is known that the solution loses regularity at a finite time $t_0$, where…
Wyman's less known static and spherically symmetric solution of the Einstein-Klein-Gordon equations and its recent generalization for positive cosmological constant are discussed, showing that they contain central naked singularities. By…
Static, spherically symmetric configurations of gravity with nonminimally coupled scalar fields are considered in D-dimensional space-times in the framework of generalized scalar-tensor theories. We seek special cases when the system has no…
We consider the Cauchy problem in the whole space for strongly damped Klein-Gordon equations. We derive asymptotic profles of solutions with weighted initial data by a simple method introduced by R. Ikehata. The obtained results show that…
Generalized solutions of the Cauchy problem for the one-dimensional periodic nonlinear Schr\"odinger equation, with certain nonlinearities, are not unique. For any $s<0$ there exist nonzero generalized solutions varying continuously in the…