Related papers: Contact Blow-Up
We develop a hybrid scheme based on a finite difference scheme and a rescaling technique to approximate the solution of nonlinear wave equation. In order to numerically reproduce the blow-up phenomena, we propose a rule of scaling…
In this paper we report on numerical studies of formation of singularities for the semilinear wave equations with a focusing power nonlinearity $u_{tt} - \Delta u = u^{p}$ in three space dimensions. We show that for generic large initial…
We establish the optimal regularity for solutions to the multiple membranes problem, and perform a blow-up analysis at points on the free boundary with the highest multiplicity. This leads to a complete classification of blow-up profiles in…
Because the interaction is well-known, Coulomb excitation is one of the best tools for the investigation of nuclear properties. In the last 3 decades new reaction theories for Coulomb excitation have been developed such as: (a) relativistic…
There are many striking phenomena which are attributed to ``quantum coherence''. It is natural to wonder if there are new quantum coherence effects waiting to be discovered which could lead to interesting results and perhaps even practical…
We study coherent enhancement of Coulomb excitation of high energy particles in crystals. We develop multiple scattering theory description of coherent excitation which consistently incorporates both the specific resonant properties of…
We present results for finite time blow-up for filtration problems with nonlinear reaction under appropriate assumptions on the nonlinearities and the initial data. In particular, we prove first finite time blow up of solutions subject to…
We study the interaction between the stability, and the propagation of regularity, for solutions to the incompressible 3D Euler equation. It is still unknown whether a solution with smooth initial data can develop a singularity in finite…
Consideration here is a generalized $\mu$-type integrable equation, which can be regarded as a generalization to both the $\mu$-Camassa-Holm and modified $\mu$-Camassa-Holm equations. It is shown that the proposed equation is formally…
A Bell inequality defined for a specific experimental configuration can always be extended to a situation involving more observers, measurement settings or measurement outcomes. In this article, such "liftings" of Bell inequalities are…
A review is given of the theoretical expectations of the self couplings of gauge bosons and of the present experimental information on the couplings. The possibilities for future measurements are also discussed.
In the context of Born-Infeld electrodynamics, the electromagnetic fields interact with each other via their non-linear couplings. A calculation will be performed where an incoming electromagnetic plane wave scatters off a Coulomb Field in…
We identify the blow-up rate of a solution to a generalised Blasius equation, that we came across while studying a probabilistic model of "Poissonian burning" in Euclidean space. Our proof involves the study of the long-time behaviour of…
This paper is concerned with the compactness of metrics of the disk with prescribed Gaussian and geodesic curvatures. We consider a blowing-up sequence of metrics and give a precise description of its asymptotic behavior. In particular, the…
We study the possibility of non-simultaneous blow-up for positive solutions of a coupled system of two semilinear equations, $u_t = J*u-u+ u^\alpha v^p$, $v_t =\Delta v^+u^qv^\beta$, $p, q, \alpha, \beta>0$ with homogeneous Dirichlet…
It is shown that third-order 1D nonlinear dispersion equations admit single point gradient catastrophe, described by blow-up-type similarity solutions. After blow-up, the solutions admit shock wave-type self-similar extensions. Snce such…
We give simple characterizations of contact 1-forms in terms of Dirac structures. We also relate normal almost contact structures to the theory of Dirac structures.
Blowup equations and holomorphic anomaly equations are two universal yet completely different approaches to solve refined topological string theory on local Calabi-Yau threefolds corresponding to A- and B-model respectively. The former…
In this paper, we consider a blow-up solution for the complex-valued semilinear wave equation with power nonlinearity in one space dimension. We first characterize all the solutions of the associated stationary problem as a two-parameter…
For arbitrary values of a parameter $\lambda\in R$, finite-time blow-up of solutions to the generalized, inviscid Proudman-Johnson equation is studied via a direct approach which involves the derivation of representation formulae for…