Related papers: Uniqueness of a Negative Mode About a Bounce Solut…
Relying on the analysis of characteristics, we prove the uniqueness of conservative solutions to the variational wave equation $u_{tt}-c(u) (c(u)u_x)_x=0$. Given a solution $u(t,x)$, even if the wave speed $c(u)$ is only H\"older continuous…
We consider an inverse boundary value problem for diffusion equations with multiple fractional time derivatives. We prove the uniqueness in determining a number of fractional time-derivative terms, the orders of the derivatives and…
We give canonical resolutions of singularities of several cone varieties arising from invariant theory. We establish a connection between our resolutions and resolutions of singularities of closure of conjugacy classes in classical Lie…
We consider an inverse problem for an inhomogeneous wave equation with discrete-in-time sources, modeling a seismic rupture. We assume that the sources occur along a path with subsonic velocity, and that data are collected over time on some…
This paper studies the existence of minimal solutions to two-point boundary value problems for quasi-monotone dynamical systems. Specifically, the pointwise infimum of all supersolutions is shown to coincide with the minimal solution. This…
We calculate the negative integer moments of the (regularized) characteristic polynomials of N x N random matrices taken from the Gaussian Orthogonal Ensemble (GOE) in the limit as $N \to \infty$. The results agree nontrivially with a…
We point out several subtleties arising in brane-world scenarios of cosmological constant cancellation. We show that solutions with curvature singularities are inconsistent, unless the contribution to the effective four-dimentional…
In this paper, we study the qualitative properties of single blow-up solutions to the nonlocal equations with slightly subcritical exponents \begin{equation*} -\Delta u=(|x|^{-(n-2)}\ast u^{p-\epsilon})u^{p-1-\epsilon}\quad…
In this work, following our recent findings in [1], we extend our analysis to explore the generalization of spherically symmetric and static black-bounce solutions, known from General Relativity, within the framework of the $f(R)$ theory in…
We present an exact analytical bouncing solution for a closed universe filled with only one exotic fluid with negative pressure, obeying a Generalized Equations of State (GEoS) of the form $P(\rho)=A\rho+B\rho^{\lambda}$, where $A$, $B$ and…
We consider the single eigenvalue fluctuations of random matrices of general Wigner-type, under a one-cut assumption on the density of states. For eigenvalues in the bulk, we prove that the asymptotic fluctuations of a single eigenvalue…
In this paper, we consider the problem of identifying a single moving point source for a three-dimensional wave equation from boundary measurements. Precisely, we show that the knowledge of the field generated by the source at six different…
The "black-bounce" spacetime geometries, were recently proposed in [A. Simpson, M. Visser, JCAP 02 (2019) 042] as regular black holes that bouncing into a future incarnation of the universe. In this work we will present several black-bounce…
This paper analyzes the inverse problem of deautoconvolution in the multi-dimensional case with respect to solution uniqueness and ill-posedness. Deautoconvolution means here the reconstruction of a real-valued $L^2$-function with support…
This paper investigates the existence of positive solutions for regular discrete second-order single-variable boundary value problems with mixed boundary conditions, including a nonhomogeneous Dirichlet boundary condition, of the form:…
We study a singular Hamiltonian system with an $\al$-homogeneous potential that contains, as a particular case, the classical $N$--body problem. We introduce a variational Morse--like index for a class of collision solutions and, using the…
The seminal work \cite{bm} by Brezis and Merle showed that the bubbling solutions of the mean field equation have the property of mass concentration. Recently, Lin and Tarantello in \cite{lt} found that the "bubbling implies mass…
We consider a variational problem with boundary singularity and Dirichlet condition. We give a blow-up analysis for sequences of solutions of an equation with exponential nonlinearity. Also, we derive a compactness criterion under some…
The catastrophic decay of a spacetime with compact dimensions, via bubbles of nothing (BoNs), is probably a generic phenomenon. BoNs admit a 4-dimensional description as singular Coleman-de Luccia bounces of the size modulus field,…
This paper summarizes the results at the present moment about singularities with respect to the Mather-Jacobian log discrepancies over algebraically closed field of arbitrary characteristic. The basic point is the Inversion of Adjunction…