Global existence and blow-up for the viscoelastic damped wave equation on the Heisenberg group
The purpose of this article is to study the Cauchy problem for the viscoelastic damped wave equation on the Heisenberg group. We first prove the global existence of small data solutions for $p\in [2,Q/(Q-4)]$ if $n=2,3$, $p>2$ if $n=1 $ using the contraction principle. Then, a blow-up result is o...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2025-07-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2025/71/abstr.html |
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| Summary: | The purpose of this article is to study the Cauchy problem for the viscoelastic
damped wave equation on the Heisenberg group.
We first prove the global existence of small data solutions for
$p\in [2,Q/(Q-4)]$ if $n=2,3$, $p>2$ if $n=1 $ using
the contraction principle. Then, a blow-up result is obtained by using the
test function method under certain integral sign assumptions for the Cauchy
data when $1<p\leq1+2/(Q-1)$, where $Q=2n+2$ is the homogeneous dimension of
the Heisenberg group. Moreover, we obtain the upper bound for the lifespan of the
solution by employing a revisited test function method. |
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| ISSN: | 1072-6691 |