相关论文: On the blowup of solutions for a nonlocal multi-di…

In this article, we study the local existence of solutions for a wave equation with a nonlocal in time nonlinearity. Moreover, a blow-up results are proved under some conditions on the dimensional space, the initial data and the nonlinear…

In this article, we consider an n-dimensional parabolic partial differential equation with a smooth coefficient term in the nonlinear gradient term. This equation was first introduced and analyzed in [E. Issoglio, On a non-linear…

We study the possibility of finite-time blow-up for a two dimensional Broadwell model. In a set of rescaled variables, we prove that no self-similar blow-up solution exists, and derive some a priori bounds on the blow-up rate. In the final…

The main aim of the current work is the study of the conditions under which (finite-time) blow-up of a non-local stochastic parabolic problem occurs. We first establish the existence and uniqueness of the local-in-time weak solution for…

We study the blow-up problem of one-dimensional nonlinear heat equations. Our result shows that for a certain class of initial conditions, the solutions blow up in finite time and we characterize the asymptotic dynamics of these solutions.…

In this paper we investigate a non-linear and non-local one dimensional transport equation under random perturbations on the real line. We first establish a local-in-time theory, i.e., existence, uniqueness and blow-up criterion for…

This paper aims to investigate a multi-dimensional transport equation with nonlocal velocity and fractional dissipation.The balance between the nonlinearity and dissipation gives rise to three different cases, namely the subcritical,…

The final goal of this paper is to prove existence of local (strong) solutions to a (fully nonlinear) porous medium equation with blow-up term and nondecreasing constraint. To this end, the equation, arising in the context of Damage…

This work studies nonnegative solutions for the Cauchy, Neumann, and Dirichlet problems of a logistic type reaction-diffusion equation. The finite time blowup results for nonnegative solutions under various restrictions on the coefficients…

In this note we show finite time blow-up for a class of non-local active scalar equations on compact Riemannian manifolds. The strategy we follow was introduced by Silvestre and Vicol to deal with the one dimensional…

The question of collapse (blow-up) in finite time is investigated for the two-dimensional (non-integrable) space-time nonlocal nonlinear Schrodinger equations. Starting from the two-dimensional extension of the well known AKNS q,r system,…

In this paper we consider the nonlinear dispersive wave equation on the real line, $u_t-u_{txx}+[f(u)]_x-[f(u)]_{xxx}+\bigl[g(u)+\frac{f''(u)}{2}u_x^2\bigr]_x=0$, that for appropriate choices of the functions $f$ and $g$ includes well known…

This paper deals with nonlinear parabolic equation for which a local solution in time exists and then blows up in a finite time. We consider the Chipot-Weissler equation. We study the numerical approximation, we show that the numerical…

We consider the nonlinear Schr\"{o}dinger equation with $L^{2}$-supercritical and $H^{1}$-subcritical power type nonlinearity. Duyckaerts and Roudenko and Campos, Farah, and Roudenko studied the global dynamics of the solutions with same…

The finite time blow-up of solutions for 1-D NLS with oscillating nonlinearities is shown in two domains: (1) the whole real line where the nonlinear source is acting in the interior of the domain and (2) the right half-line where the…

We study the Cauchy problem for a system of two coupled nonlinear focusing Schroedinger equations arising in nonlinear optics. We discuss when the solutions are global in time or blow-up in finite time. Some results, in dependence of the…

The aim of this paper is to study the finite space blow up of the solutions for a class of fourth order differential equations. Our results answer a conjecture in [F. Gazzola and R. Pavani. Wide oscillation finite time blow up for solutions…

We investigate a system of nonlocal transport equations in one spatial dimension. The system can be regarded as a model for the 3D Euler equations in the hyperbolic flow scenario. We construct blowup solutions with control up to the blowup…

In a previous work with Tai-Peng Tsai, the author studied the dynamics of axisymmetric, swirl-free Euler equation in four and higher dimensions. One conclusion of this analysis is that the dynamics become dramatically more singular as the…

We consider a family of non-local problems that model the effects of transport and vortex stretching in the incompressible Euler equations. Using modulation techniques, we establish stable self-similar blow-up near a family of known…