Related papers: Sharp non-explicit blow-up profile for perturbed n…
We deal with existence and non-existence of non-negative entire solutions that blow-up at infinity for a quasilinear problem depending on a non-negative real parameter. Our main objectives in this paper are to provide far more general…
We classify the finite time blow-up profiles for the following reaction-diffusion equation with unbounded weight: $$ \partial_tu=\Delta u^m+|x|^{\sigma}u^p, $$ posed in any space dimension $x\in\mathbf{R}^N$, $t\geq0$ and with exponents…
We consider in this paper some class of perturbation for the semilinear wave equation with critical (in the conformal transform sense) power nonlinearity. Working in the framework of similarity variables, we find a Lyapunov functional for…
We establish the first complete classification of finite-time blow-up scenarios for strong solutions to the three-dimensional incompressible Euler equations with surface tension in a bounded domain possessing a closed, moving free boundary.…
We consider the following parabolic system whose nonlinearity has no gradient structure: $$\left\{\begin{array}{ll} \partial_t u = \Delta u + e^{pv}, \quad & \partial_t v = \mu \Delta v + e^{qu}, u(\cdot, 0) = u_0, \quad & v(\cdot, 0) =…
The phenomenon of finite time blow-up in hydrodynamic partial differential equations is central in analysis and mathematical physics. While numerical studies have guided theoretical breakthroughs, it is challenging to determine if the…
In this paper we consider a system of equations that describes a class of mass-conserving aggregation phenomena, including gravitational collapse and bacterial chemotaxis. In spatial dimensions strictly larger than two, and under the…
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…
We establish uniform a priori estimates for solutions of semilinear planar Hamiltonian elliptic systems in a ball with Dirichlet boundary conditions. We consider a broad class of coupled nonlinearities with asymptotic critical behaviour in…
We investigate blow-up phenomena for positive solutions of nonlinear reaction-diffusion equations including a nonlinear convection term $\partial_t u = \Delta u - g(u) \cdot \nabla u + f(u)$ in a bounded domain of $\mathbb{R}^N$ under the…
In this note, we prove a blow-up result for the semilinear damped wave equation in a compact Lie group with power nonlinearity $|u|^p$ for any $p>1$, under suitable integral sign assumptions for the initial data, by using an iteration…
We prove that arbitrary smooth perturbations of the zero equilibrium state of the repulsive pressureless Euler-Poisson equations, which describe the behavior of cold plasma, blow up for any non-constant doping profile already in…
In this paper, we study the blow-up of solutions for semilinear wave equations with scale-invariant dissipation and mass in the case in which the model is somehow 'wave-like'. A Strauss type critical exponent is determined as the upper…
We consider the semilinear heat equation $u_t - \Delta u = f(u)$ in $\Omega = B_R(0) \subset \mathbb{R}^n$ with super-exponential nonlinearities $f(u) = e^{u^p}u^q$ ($p>1$, $q \in \{0\}\cup [1,\infty)$), nonnegative bounded radially…
We investigate finite-time blow-up of solutions to the Cauchy problem for a semilinear heat equation posed on infinite graphs. Assuming that the initial datum is sufficiently large, we establish a general blow-up criterion valid on…
In this paper we consider the blow-up for solutions to a weakly coupled system of semilinear damped wave equations of derivative type in the scattering case. After introducing suitable functionals proposed by Lai-Takamura for the…
A nonlinear profile decomposition is established for solutions of supercritical generalized Korteweg-de Vries equations. As a consequence, we obtain a concentration result for finite time blow-up solutions that are of Type II.
This paper deals with unbounded solutions to a class of chemotaxis systems. In particular, for a rather general attraction-repulsion model, with nonlinear productions, diffusion, sensitivities and logistic term, we detect Lebesgue spaces…
We establish the local existence and the uniqueness of solutions of the heat equation with a nonlinear boundary condition for the initial data in uniformly local $L^r$ spaces. Furthermore, we study the sharp lower estimates of the blow-up…
We consider the energy super critical $d+1$ dimensional semilinear heat equation $$\partial_tu=\Delta u+u^{p}, \ \ x\in \Bbb R^{d+1}, \ \ p\geq 3, \ d\geq 14.$$ A fundamental open problem on this canonical nonlinear model is to understand…