Related papers: Contact Blow-Up

In this brief review we discuss the basic theoretical concepts used in the experimental studies of the most common cases of direct reactions such as (a) elastic scattering, (b) inelastic scattering, (c) Coulomb excitation, (d) transfer…

Fifth-order 1D nonlinear dispersion equations are shown to admit blow-up formation of shock waves as well as rarefaction waves. The concepts of smooth deformations are applied to distinguish "entropy" shocks from smooth rarefaction waves.…

1. Quantized conductance 2. When 1 mode = 1 atom 3. Photons and Cooper pairs 4. Thermal analogues 5. Shot noise 6. Solid-state electron optics 7. Ultimate confinement 8. Landauer formulas

n a number of papers it was shown that there are one-dimensional systems such that they contain solutions with, so called, overcompressive singular shock waves besides the usual elementary waves (shock and rarefaction ones as well as…

The present paper concerns with the existence of blow-up solution for a class of elliptic system with convection term. Here, we prove a result involving sub and supersolution for a class of elliptic system whose nonlinearity can depend of…

In this paper we apply the differential inequality technique of Payne {\it et. al} \cite{Payne&SchaeferRobin08} to show that a reaction-diffusion system admits blow-up solutions, and to determine an upper bound for the blow-up time. For a…

The fundamental quantities of potential scattering theory are generalized to accommodate long-range interactions. New definitions for the scattering amplitude and wave operators valid for arbitrary interactions including potentials with a…

We consider spherically symmetric supercritical focusing wave equations outside a ball. Using mixed analytical and numerical methods, we show that the threshold for blowup is given by a codimension-one stable manifold of the unique static…

We study blow-ups in generalized complex geometry. To that end we introduce the concept of holomorphic ideal, which allows one to define a blow-up in the category of smooth manifolds. We then investigate which generalized complex…

It has been known for a long time that the equivariant 2+1 wave map into the 2-sphere blows up if the initial data are chosen appropriately. Here, we present numerical evidence for the stability of the blow-up phenomenon under explicit…

In this paper, we present a formula describing the formation and decay of shock wave type solutions in some special cases.

We study finite-time singularities in the linear advection-diffusion equation with a variable speed on a semi-infinite line. The variable speed is determined by an additional condition at the boundary, which models the dynamics of a contact…

A class of equations with exponential nonlinearities on a compact Riemannian surface is considered. More precisely, we study an asymmetric sinh-Gordon problem arising as a mean field equation of the equilibrium turbulence of vortices with…

We give a systematic treatment to the concept of hypoellipticity, putting it into an abstract form which allows us to deal with several different notions within the same framework. We then investigate when a notion of hypoellipticity…

We consider the semilinear wave equation in the radial case with conformal subcritical power nonlinearity. If we consider a blow-up point different from the origin, then we exhibit a new Lyapunov functional which is a perturbation of the…

We provide a numerical validation method of blow-up solutions for finite dimensional vector fields admitting asymptotic quasi-homogeneity at infinity. Our methodology is based on quasi-homogeneous compactifications containing a new…

Hypothesis: Immiscible liquids are commonly used to achieve unique functions in many applications, where the breakup of compound droplets in airflow is an important process. Due to the existence of the liquid-liquid interface, compound…

We consider a sequence of blowup solutions of a two dimensional, second order elliptic equation with exponential nonlinearity and singular data. This equation has a rich background in physics and geometry. In a work of…

We describe blow-up behavior for ODEs by means of dynamics at infinity with complex asymptotic behavior in autonomous systems, as well as in nonautonomous systems. Based on preceding studies, a variant of closed embeddings of phase spaces…

We prove that intersection multiplicity of two plane curves defined by Fulton's axioms is equivalent to the multiplicity computed using blowup. The algorithm based on the latter is presented and its complexity is estimated. We compute for…