Related papers: Dynamical behavior near explicit self-similar blow…
We consider in this paper some class of perturbation for the semilinear wave equation with subcritical (in the conformal transform sense) power nonlinearity. We first derive a Lyapunov functional in similarity variables and then use it to…
We consider co-rotational wave maps from (1+3)-dimensional Minkowski space into the three-sphere. This model exhibits an explicit blowup solution and we prove the asymptotic nonlinear stability of this solution in the whole space under…
We consider in this paper a class of strongly perturbed semilinear wave equations with a non-characteristic point in one space dimension, for general initial data. Working in the framework of similarity variables, in \cite {MZ} Merle and…
In an abstract Banach space we study conditions for the existence of piecewise continuous, almost periodic solutions for semi-linear impulsive differential equation with fixed and non-fixed moments of impulsive action
We propose a new model of nonlinear electrodynamics with three parameters. Born-Infeld electrodynamics and exponential electrodynamics are particular cases of this model. The phenomenon of vacuum birefringence is studied. We show that there…
We consider wave maps from the $(1+d)$-dimensional Minkowski space into the $d$-sphere. It is known from the work of Bizo\'n and Biernat \cite{BizBie15} that in the energy-supercritical case, i.e., for $d \geq 3$, this model admits a…
In this paper, we deal with existence, uniqueness and exact rate of boundary behavior of blow-up solutions for a class of logistic type quasilinear problem in a smooth bounded domain involving the $p$-Laplacian operator, where the…
We study the asymptotic behavior of complex discrete evolution equations of Ginzburg- Landau type. Depending on the nonlinearity and the data of the problem, we find different dynamical behavior ranging from global existence of solutions…
We investigate the dynamics of the localized nonlinear matter wave in spin-1 Bose-Einstein condensates with trapping potentials and nonlinearities dependent on time and space. We solve the three coupled Gross-Pitaevskii equation by…
We consider positive radial decreasing blow-up solutions of the semilinear heat equation \begin{equation*} u_t-\Delta u=f(u):=e^{u}L(e^{u}),\quad x\in \Omega,\ t>0, \end{equation*} where $\Omega=\mathbb{R}^n$ or $\Omega=B_R$ and $L$ is a…
The question of spontaneous apparition of singularity in the 3D incompressible Euler equations is one of the most important and challenging open problems in mathematical fluid mechanics. In this survey article we review some of recent…
We provide several characterizations of convergence to unstable equilibria in nonlinear systems. Our current contribution is three-fold. First we present simple algebraic conditions for establishing local convergence of non-trivial…
In whatever Lorentz invariant theory, the presence of extended d-dimensional objects inside a higher dimensional bulk space-time, like for instance D-branes in string theories, induces a spontaneous breakdown of the Poincare' invariance of…
Consider a smooth, bounded domain $\O\subset \mathbb{R}^n$ with $n\geq 4$ and a smooth positive function $V$. We analyze the asymptotic behavior of a sequence of positive solutions $u_\e$ to the equation $-\Delta u +V(x)u…
We consider $u(x,t)$, a solution of $\partial_tu = \Delta u + |u|^{p-1}u$ which blows up at some time $T > 0$, where $u:\mathbb{R}^N \times[0,T) \to \mathbb{R}$, $p > 1$ and $(N-2)p < N+2$. Define $S \subset \mathbb{R}^N$ to be the blow-up…
This paper is concerned with strong blow-up instability (Definition 1.3) for standing wave solutions to the system of the quadratic nonlinear Klein-Gordon equations. In the single case, namely the nonlinear Klein-Gordon equation with power…
We use the abelian Born-Infeld action for the worldvolume gauge field and transverse displacement scalars to explore new aspects of D-brane structure and dynamics. We study several classic gauge field configurations, including point charges…
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 study the formation of singularity for the isothermal Euler-Poisson system arising from plasma physics. Contrast to the previous studies yielding only limited information on the blow-up solutions, for instance, sufficient conditions for…
In this note we research the Abelian Higgs model subject to the Born-Infeld theory of electrodynamics for which the BPS equations can be reduced into a quasi-linear differential equation. We show that the equation exists a unique solution…