We consider in this paper a perturbation of the standard semilinear heat equation by a term involving the space derivative and a non-local term. In some earlier work [1], we constructed a blow-up solution for that equation, and showed that it blows up (at least) at the origin. We also derived the so called "intermediate blow-up profile". In this paper, we prove the single point blow-up property and determine the final blow-up profile.

中文翻译：

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具有梯度和非局部项的扰动非线性热方程的单点膨胀和最终轮廓

我们在本文中考虑了标准半线性热方程的扰动，其中涉及空间导数和非局部项。在一些早期的工作中 [1]，我们为该方程构建了一个爆炸解，并表明它（至少）在原点爆炸。我们还推导出了所谓的“中间爆破剖面”。在本文中，我们证明了单点爆破特性并确定了最终的爆破剖面。