Related papers: Blow-Up for Nonlinear Wave Equations describing Bo…
This is the first of two papers devoted to the study of the properties of the blow-up surface for the $N$ dimensional semilinear wave equation with subconformal power nonlinearity. In a series of papers, we have clarified the situation in…
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 construct a one parameter family of finite time blow ups to the co-rotational wave maps problem from $S^2\times \RR$ to $S^2,$ parameterized by $\nu\in(1/2,1].$ The longitudinal function $u(t,\alpha)$ which is the main object of study…
This paper investigates the blow-up of solutions to scale-invariant semilinear wave equations featuring the damping term $\frac{\mu}{1+t} \partial_t u$, the mass term $\frac{\nu^2}{(1+t)^2} u$, and a time-derivative nonlinearity $|…
This paper studies a nonlinear plate equation with internal fractional damping and a time-delay term, driven by a polynomial-type nonlinear source. Such a model arises naturally in the description of viscoelastic and feedback-controlled…
In this manuscript the three types of late-time behavior of spherically symmetric Boson Stars are presented, these are: stable configurations, unstable bounded that collapse to form black holes and unstable unbounded that explode. The…
The study of blow-up solution of time-fractional heat equations is of significant and wide-ranging interest for its multitude of applications. These types of equations are used to model several real problems in science and engineering. This…
We consider the semilinear diffusion equation $\partial$ t u = Au + |u| $\alpha$ u in the half-space R N + := R N --1 x (0, +$\infty$), where A is a linear diffusion operator, which may be the classical Laplace operator, or a fractional…
In this paper, we consider a semilinear parabolic equation with nonlinear nonlocal Neumann boundary condition and nonnegative initial datum. We first prove global existence results. We then give some criteria on this problem which determine…
We prove that solutions to the critical wave equation below can not be global if the initial values are positive somewhere and nonnegative. This completes the solution to the famous blow up conjecture about critical semilinear wave…
Gauged boson stars are exotic compact objects that can potentially mimic black holes or magnetized neutron stars in both their gravitational and electromagnetic signatures, offering a compelling new description or even an alternative…
In this paper we study blow-up phenomena in general coupled nonlinear Schrodinger equations with different dispersion coefficients. We find sufficient conditions for blow-up and for the existence of global solutions. We discuss several…
This paper deals with isothermal Euler-Poisson system which is used to model collapse of self-gravitating Newtonian star. Density dependent viscosity term is added on the right-hand side of momentum equation and it has been proved that…
We consider the semilinear heat equation \begin{equation}\label{problemAbstract}\left\{\begin{array}{ll}v_t-\Delta v= |v|^{p-1}v & \mbox{in}\Omega\times (0,T)\\ v=0 & \mbox{on}\partial \Omega\times (0,T)\\ v(0)=v_0 & \mbox{in}\Omega…
We consider the following nonlinear Schr\"{o}dinger equation with a Hartree nonlinearity: \[ i\frac{\partial u}{\partial t}+\Delta u+|u|^{\frac{4}{N}}u\pm\left(\frac{1}{|x|^{2\sigma}}\star|u|^2\right)u=0 \] in $\mathbb{R}^N$. We are…
We show the existence of a new class of initially smooth spherically symmetric self-similar solutions to the non-isentropic Euler-Poisson system. These solutions exhibit supersonic gravitational implosion in the sense that the density…
In this paper, we consider the following semi-linear complex heat equation \begin{eqnarray*} \partial_t u = \Delta u + u^p, u \in \mathbb{C} \end{eqnarray*} in $\mathbb{R}^n,$ with an arbitrary power $p,$ $ p > 1$. In particular, $p$ can be…
We study solutions close to solitary waves of the pseudo-relativistic Hartree equation describing boson stars under the influence of an external gravitational field. In particular, we analyze the long-time effective dynamics of such…
We study stable blow-up dynamics in the generalized Hartree equation with radial symmetry, a Schr\"odinger-type equation with a nonlocal, convolution-type nonlinearity: $iu_t+\Delta u +\left(|x|^{-(d-2)} \ast |u|^{p} \right) |u|^{p-2}u = 0,…
We begin to study in this paper orbital and asymptotic stability of standing waves for a model of Schr\"odinger equation with concentrated nonlinearity in dimension three. The nonlinearity is obtained considering a {point} (or contact)…