Related papers: Uniqueness for bubbling solutions with collapsing …
Existence of mass-conserving weak solutions to the coagulation-fragmentation equation is established when the fragmentation mechanism produces an infinite number of fragments after splitting. The coagulation kernel is assumed to increase at…
Very differently from those perturbative techniques of Deng-Musso in [26], we use the assumption of a $C^1$-stable critical point to construct positive or sign-changing solutions with arbitrary $m$ isolated bubbles to the boundary value…
For a bounded set $\Omega \subset \mathbb R^N$ and a perturbation $V \in C^1(\overline{\Omega})$, we analyze the concentration behavior of a blow-up sequence of positive solutions to \[ -\Delta u_\epsilon + \epsilon V = N(N-2)…
The nonlocal nonlinear aggregation equation in one space dimension is investigated. In the so-called attractive case smooth solutions blow up in finite time, so that weak measure solutions are introduced. The velocity involved in the…
In this paper, we consider the Brezis-Nirenberg problem $$ -\Delta u=\lambda u+|u|^{\frac{4}{N-2}}u,\quad\mbox{in}\,\, \Omega,\quad u=0,\quad\mbox{on}\,\, \partial\Omega, $$ where $\lambda\in\mathbb{R}$, $\Omega\subset\mathbb R^N$ is a…
An existence result on weak solutions to the continuous coagulation equation with collision-induced multiple fragmentation is established for certain classes of unbounded coagulation, collision and breakup kernels. In this model, a pair of…
We show global uniqueness of the solution to a class of constrained variational problems, using scaling properties. This is used to establish the essential uniqueness of solutions of a large deviations problem in multiple dimensions. The…
In this paper we study the continuous coagulation and multiple fragmentation equation for the mean-field description of a system of particles taking into account the combined effect of the coagulation and the fragmentation processes in…
In this paper we explore the idea that black holes can persist in a universe that collapses to a big crunch and then bounces into a new phase of expansion. We use a scalar field to model the matter content of such a universe {near the time}…
We formulate a martingale problem that describes a diffusion process in a multidimensional Euclidean space with a membrane located on a given smooth surface and having the properties of skewing and delaying. The theorem on the existence of…
Global weak solutions to the continuous Smoluchowski coagulation equation (SCE) are constructed for coagulation kernels featuring an algebraic singularity for small volumes and growing linearly for large volumes, thereby extending previous…
When an asymmetric bubble collapses it generally produces a well defined high velocity jet. This is remarkable because one might expect such a collapse to produce a complex or chaotic flow rather than an ordered one. I present a dimensional…
In spherical symmetry compelling numerical evidence suggests that in general relativity solutions near the threshold of black hole formation exhibit critical behavior. One aspect of this is that threshold solutions themselves are…
Bubbles are point-like regular solutions of the higher-dimensional Kaluza-Klein equations that appear as naked singularities in four dimensions. We analyze all such possible solutions in 5D Kaluza-Klein theory that are static and…
In general, to avoid a singularity in cosmological models involves the introduction of exotic kind of matter fields, for example, a scalar field with negative energy density. In order to have a bouncing solution in classical General…
The inertial collapse of two interacting and non-translating spherical bubbles of equal size is considered. The exact analytic solution to the nonlinear ordinary differential equation that governs the bubble radii during collapse is first…
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 evolution of bubble spacetimes in vacuum and electrovac scenarios by numerical means. We find strong evidence against the formation of naked singularities in (i) scenarios with negative masses displaying initially collapsing…
Possibilities emerging out of the dynamical evolutions of collapsing systems are addressed in this thesis through analytical investigations of the highly non-linear Einstein Field Equations. Studies of exact solutions and their properties,…
We establish the non-degeneracy of bubbling solutions for singular mean field equations when the blow-up points are either regular or involve non-quantized singular sources. This extends the results from Bartolucci-Jevnikar-Lee-Yang…