Related papers: Blowup solutions for stochastic parabolic equation…
In this paper, we study blow up behavior of the semilinear parabolic inequality with $p$-Laplacian operator and nonlinear source $u_t - \Delta_p u \geq \sigma(x, t)\Phi(u)$ on a locally finite connected weighted graph $G = (V, E)$. We…
We establish a link between stability estimates for a hyperbolic inverse problem via the Boundary Control method and the blowup of a constant appearing in the contexts of optimal unique continuation and cost of approximate controllability.
We consider a nonlocal parabolic PDE, which may be regarded as the standard semilinear heat equation with power nonlinearity, where the nonlinear term is divided by some Sobolev norm of the solution. In this paper, we are interested in…
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…
We consider the wave equation with a focusing cubic nonlinearity in higher odd space dimensions without symmetry restrictions on the data. We prove that there exists an open set of initial data such that the corresponding solution exists in…
In this note, we consider the blowup phenomenon of Grushin's operator. By using the knowledge of probability, we first get expression of heat kernel of Grushin's operator. Then by using the properties of heat kernel and suitable auxiliary…
The blowup is studied for the nonlinear Schr\"{o}dinger equation $iu_{t}+\Delta u+ |u|^{p-1}u=0$ with $p$ is odd and $p\ge 1+\frac 4{N-2}$ (the energy-critical or energy-supercritical case). It is shown that the solution with negative…
In this work we determine the critical exponent for a weakly coupled system of semilinear wave equations with distinct scale-invariant lower order terms, when these terms make both equations in some sense parabolic-like. For the blow-up…
In this paper we study the behavior of a class of mild solutions of the homogeneous and isotropic bosonic Boltzmann-Nordheim equation near the blow-up. We obtain some estimates on the blow-up rate of the solutions and prove that, as long as…
We examine a 2-dimensional ODE which exhibits explosion in finite time. Considered as an SDE with additive white noise, it is known to be complete - in the sense that for each initial condition there is almost surely no explosion.…
In this paper we give a sharper condition for the blow-up of the solution to a nonlinear Schroedinger equation with free/Stark/quadratic potential by improving the well known Zakharov-Glassey's method.
In this article, we investigate the blow-up behavior of solutions to the one-dimensional damped nonlinear wave equation, namely $$ \partial_t^2 u - \partial_x^2 u + \frac{\mu}{1 + t} \partial_t u = |\partial_t u|^p \quad (p > 1). $$ Under…
In this short note, we present a construction for the log-log blow up solutions to focusing mass-critical stochastic nonlinear Schr\"oidnger equations with multiplicative noises. The solution is understood in the sense of controlled rough…
We give a blow-up behavior for solutions to a problem with singularity and with Dirichlet condition. An application, we have a compactness of the solutions to this Problem with singularity and Lipschitz conditions.
The study of nonlinear waves that collapse in finite time is a theme of universal interest, e.g. within optical, atomic, plasma physics, and nonlinear dynamics. Here we revisit the quintessential example of the nonlinear Schrodinger…
Gaussians to study soliton behavior and blowup in the nonlinear Schrodinger equation in arbitrary dimension d and with arbitrary nonlinearity parameter kappa
We construct examples of finite time singularity from smooth data for linear uniformly parabolic systems in the plane. We obtain similar examples for quasilinear systems with coefficients that depend only on the solution.
We investigate the local existence, finite time blow-up and global existence of sign-changing solutions to the inhomogeneous parabolic system with space-time forcing terms $$ u_t-\Delta u =|v|^{p}+t^\sigma w_1(x),\,\, v_t-\Delta v…
We first establish local well-posedness for a periodic 2-component Camassa-Holm equation with vorticity. We then present a global existence result for strong solutions to the equation. We finally obtain several blow-up results and the…
In this work we derive some blow-up results for semilinear wave equations both in de Sitter and anti-de Sitter spacetimes. By requiring suitable conditions on a time-dependent factor in the nonlinear term, we prove the blow-up in finite…