基于欧姆加热模型的一类非局部双曲方程解的渐近性态

In this paper,the asymptotic behavior of a non-local hyperbolic problem modelling Ohmic heating is studied.It is found that the behavior of the solution of the hyperbolic problem only has three cases:the solution is globally bounded and the unique steady state is globally asymptotically stable;the solution is infinite when t→∞;the solution blows up.If the solution blows up,the blow-up is uniform on any compact subsets of(0,1] and the blow-up rate is lim t → T*-u(x,t)(T*-t)1/α+βp-1=(α+βp-1/1-α)1/1-α-βp,where T* is the blow-up time.

Asymptotic Behavior of a Non-Local Hyperbolic Equation Modelling Ohmic Heating

In this paper, the asymptotic behavior of a non-local hyperbolic problem modelling Ohmic heating is studied. It is found that the behavior of the solution of the hyperbolic problem only has three cases: the solution is globally bounded and the unique steady state is globally asymptotically stable; the solution is infinite when $trightarrowinfty$; the solution blows up. If the solution blows up, the blow-up is uniform on any compact subsets of $(0,1]$ and the blow-up rate is $lim_{trightarrow T^{*}-}u(x,t)(T^{*}-t)^{frac{1}{alpha+beta p-1}}=(frac{alpha+beta p-1} {1-alpha})^{frac{1}{1-alpha-beta p}}$, where $T^{*}$ is the blow-up time.