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We consider the incompressible Euler equations in two or three dimensions and we show that the addition of a suitable multiplicative It? noise with superlinear growth prevents a smooth solution from b...
We first establish local well-posedness for a periodic 2-component Camassa-Holm equation. We then present two global existence results for strong solutions to the equation. We finally obtain several b...
Abstract: We establish a blow-up criterion in terms of the upper bound of the density and temperature for the strong solution to 2D compressible viscous heat-conductive flows. The initial vacuum is al...
Abstract: It is shown that Wiener's regularity of the vertex of a backward paraboloid for 3D Navier-Stokes equations with zero Dirichlet conditions on the paraboloid boundary is given by Petrovskii's ...
Abstract: In this paper, the discretization of a nonlinear wave equation whose nonlinear term is a power function is introduced. The difference equation derived by discretizing the nonlinear wave equa...
Countable families of global-in-time and blow-up similarity sign-changing patterns of the Cauchy problem for the fourth-order thin film equation (TFE–4) ut = −∇ · (|u|n∇u) in RN × R...
Considered herein are the generalized Camassa-Holm and Degasperis-Procesi equations in the spatially periodic setting. The pre-cise blow-up scenarios of strong solutions are derived for both of equa-t...
We study the initial-value problem for a general class of nonlinear nonlocal coupled wave equations. The problem involves convolution operators with kernel functions whose Fourier transforms are nonne...
讨论了 (f)单调增加的条件下,具有非线性记忆的抛物型方程解的Blow up,并给出了解的Blow up估计。
讨论奇异半线性发展方程组解的Blow-up问题时,通常先对解进行估计,然后讨论在一定条件下解的Blow-up.论文继续用这种方法讨论奇异半线性发展方程组解的Blow-up问题,得到一定条件下解会Blow-up.
研究了非线性反应扩散方程ut =Δu+f(u)初边值问题的解的Blow-up问题,证明了其光滑解只能在一个有界区间内存在。利用引入的“高斯函数”得到了一些新的非整体存在的充分条件,这些条件对Lp解也普遍适用。此外,对有关结果进行了相应的简化与改进。
This paper is concerned with a nonlocal hyperbolic system as follows: $$\align & u_{tt}=\triangle u+\bigg( \int_\Omega vdx\bigg)^{p} \quad \textrm{for}\,\,x\in \mathbb{R}^N, \,\, t>0, \\ & v_{tt}=\tri...
本文研究了拟线性抛物型方程的初边值问题在无界区域D上的全局解存在性问题和局部解的Blow-up问题.利用上、下解方法,并借助Green函数,给出了问题(I)全局解的存在性条件,也给出了局部解发生Blowup现象的条件。

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