On the Stabilization Rate of Solutions of the Cauchy Problem for a Parabolic Equation with Lower-Order Terms
- Authors: Denisov V.N.1
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Affiliations:
- M. V. Lomonosov Moscow State University
- Issue: Vol 233, No 6 (2018)
- Pages: 807-827
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/241707
- DOI: https://doi.org/10.1007/s10958-018-3968-9
- ID: 241707
Cite item
Abstract
The following Cauchy problem for parabolic equations is considered in the half-space \( \overline{D}={\mathrm{\mathbb{R}}}^N\times \left[0,\infty \right) \), N ≥ 3:
\( {L}_1u\equiv Lu+c\left(x,t\right)u-{u}_t=0,\kern0.5em \left(x,t\right)\in D,\kern0.5em u\left(x,0\right)={u}_0(x),\kern0.5em x\in {\mathrm{\mathbb{R}}}^N. \)
It is proved that for any bounded and continuous in ℝN initial function u0(x), the solution of the above Cauchy problem stabilizes to zero uniformly with respect to x from any compact set K in ℝN either exponentially or as a power (depending on the estimate for the coefficient c(x, t) of the equation).
About the authors
V. N. Denisov
M. V. Lomonosov Moscow State University
Author for correspondence.
Email: vdenisov2008@yandex.ru
Russian Federation, Moscow