Related papers: Contact Blow-Up
We study the possibility of finite-time blow-up for a two dimensional Broadwell model. In a set of rescaled variables, we prove that no self-similar blow-up solution exists, and derive some a priori bounds on the blow-up rate. In the final…
We survey some recent results concerning the behaviour of the contact structure defined on the boundary of a complex isolated hypersurface singularity or on the boundary at infinity of a complex polynomial.
We study positive blowing-up solutions of systems of the form: $$u_t=\delta_1 \Delta u+e^{pv},\quad v_t= \delta_2\Delta v+e^{qu},$$ with $\delta_1,\delta_2>0$ and $p, q>0$. We prove single-point blow-up for large classes of radially…
An important question in mathematical relativity theory is that of the nature of spacetime singularities. The equations of general relativity, the Einstein equations, are essentially hyperbolic in nature and the study of spacetime…
Three classes of higher-order nonlinear parabolic hyperbolic, and nonlinear dispersion equations are shown to admit exact blow-up or compacton solutions, which are induced by elliptic equations with non-Lipschitz nonlinearities. Variational…
We construct a functor from the category of manifolds with generalized corners to the category of complexes of toric monoids, and for every `refinement' of the complex associated to a manifold, we show there is a unique `blow-up', i.e., a…
In this paper we develop a blow up analysis for solutions of a planar semilinear elliptic equation involving exponential nonlinearities. Such solutions describe cosmic strings, and we show how their blow up behaviour is characterised by new…
Geometric treatments of blow-up solutions for autonomous ordinary differential equations and their blow-up rates are concerned. Our approach focuses on the type of invariant sets at infinity via compactifications of phase spaces, and…
This note shows the blow-up of certain non-small solutions to relaxed compressible Navier-Stokes equations in divergence form.
Let $M$ be a real-analytic connected CR-hypersurface of CR-dimension $n>0$ having a point of Levi-nondegeneracy. The following alternative is demonstrated for both the symmetry algebra $s$ and the automorphism group $G$ of $M$. Denote by…
We review different notions of cuts appearing throughout the literature on scattering amplitudes. Despite similar names, such as unitarity cuts or generalized cuts, they often represent distinct computations and distinct physics. We…
We construct new examples of contact manifolds in arbitrarily large dimensions. These manifolds which we call quasi moment-angle manifolds, are closely related to the classical moment-angle manifolds.
This paper is concerned with finite blow-up solutions of the heat equation with nonlinear boundary conditions. It is known that a rate of blow-up solutions is the same as the self-similar rate for a Sobolev subcritical case. A goal of this…
Contact numbers are natural extensions of kissing numbers. In this paper we give estimates for the number of contacts in a totally separable packing of n unit balls in Euclidean d-space for all n>1 and d>1.
We establish a blow-up criterion in terms of the upper bound of the density and temperature for the strong solution to 2D compressible viscous heat-conductive flows. The initial vacuum is allowed.
We present a numerical study of solutions to the generalized Kadomtsev-Petviashvili equations with critical and supercritical nonlinearity for localized initial data with a single minimum and single maximum. In the cases with blow-up, we…
We associate a combinatorial object to sequences of point blow-ups over perfect fields, the weighted directed graph, and another one to the composition of all blow-ups, which we call associated sequential morphisms, the $d-$ary intersection…
This paper concerns a controllability problem for blowup points on heat equation. It can be described as follows: In the absence of control, the solution to the linear heat system globally exists in a bounded domain $\Omega$. While, for a…
In quantum communication feedback may be defined in a number of distinct ways. An analysis of the effect feedback has on the rate information may be communicated is given, and a number of results and conjectures are stated.
Blow-up rates are established for general solutions to the quasilinear diffusion equation $$ \partial_tu=\Delta u^m+|x|^{\sigma}u^p, \quad (x,t)\in\mathbb{R}^N\times(0,T), $$ in the range of exponents $1<p<m$, $\sigma>0$. More precisely, if…