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The linear heat equation with highly oscillating potential


Author: Ismail Kombe
Journal: Proc. Amer. Math. Soc. 132 (2004), 2683-2691
MSC (2000): Primary 35K15, 35K25, 35R25
DOI: https://doi.org/10.1090/S0002-9939-04-07392-7
Published electronically: April 9, 2004
MathSciNet review: 2054795
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we consider the following initial value problem:

\begin{displaymath}\begin{cases} \frac{\partial u}{\partial t}=-Hu+V(x)u & \text... ...)\geq 0 & \text{on}\quad\mathbb{R}^N \times\{t=0\}, \end{cases}\end{displaymath}

where $ H=-\Delta -\frac{\beta}{\vert x\vert^2}\sin(\frac{1}{\vert x\vert^{\alpha}}) $ and $0\le V\in L_{\text{loc}}^1(\mathbb{R}^N)$. Nonexistence of positive solutions is analyzed.


References [Enhancements On Off] (What's this?)

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Additional Information

Ismail Kombe
Affiliation: Department of Mathematics, 202 Mathematical Sciences Building, University of Missouri, Columbia, Missouri 65211
Email: kombe@math.missouri.edu

DOI: https://doi.org/10.1090/S0002-9939-04-07392-7
Keywords: Heat equation, instantaneous blow up, positive solutions
Received by editor(s): April 21, 2003
Received by editor(s) in revised form: June 18, 2003
Published electronically: April 9, 2004
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2004 American Mathematical Society

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