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首页> 外文期刊>Differential and integral equations >Blow-up and stability of a nonlocal diffusion-convection problem arising in ohmic heating of foods
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Blow-up and stability of a nonlocal diffusion-convection problem arising in ohmic heating of foods

机译：食物欧姆加热引起的非局部扩散对流问题的爆炸性和稳定性

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摘要

We study the blow-up and stability of solutions of the equation u_t + u_x = u_(xx) + λf(u)/(∫ from x = 0 to x = 1 of f(u) dx)~2 with certain initial and boundary conditions. When f is a decreasing function, we show that if ∫ from x = 0 to x = ∞ of f(s) ds < ∞, then there exists a λ~* > 0 such that for λ > λ~*, or for any 0 < λ ≤ λ~* but with initial data sufficiently large, the solutions blow up in finite time. If ∫ from x = 0 to x = ∞ to f(s) ds = ∞, then the solutions are global in time. The stability of solutions in both cases is discussed. We also study the case of f being increasing.
机译：我们研究方程u_t + u_x = u_（xx）+λf（u）/（∫从f（u）dx的x = 0到x = 1）〜2具有一定初始值和解的爆破性和稳定性边界条件。当f是一个递减函数时，我们证明如果f（s）ds <∞的从x = 0到x =∞的∫，则存在一个λ〜*> 0，使得对于λ>λ〜*或任何0 <λ≤λ〜*但初始数据足够大时，解在有限时间内爆炸。如果从x = 0到x =∞到f（s）ds =∞的∫，则解在时间上是全局的。讨论了两种情况下解决方案的稳定性。我们还研究了f增加的情况。

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