Nonexistence results for pseudo-parabolic equations in the Heisenberg group

Mohamed Jleli; Mokhtar Kirane; Bessem Samet

doi:10.1007/s00605-015-0823-7

Nonexistence results for pseudo-parabolic equations in the Heisenberg group

Mohamed Jleli, Mokhtar Kirane, Bessem Samet

Mathematics

College of Sciences

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We derive sufficient conditions for the nonexistence of global weak solutions to the nonlinear pseudo-parabolic equation (Formula presented.), where Δ_H is the Kohn–Laplace operator on the (2N + 1) -dimensional Heisenberg group H, p> 1 and f(t, ϑ) is a given function. Next, we extend this result to the case of systems. Our technique of proof is based on the test function method.

Original language	British English
Pages (from-to)	255-270
Number of pages	16
Journal	Monatshefte fur Mathematik
Volume	180
Issue number	2
DOIs	https://doi.org/10.1007/s00605-015-0823-7
State	Published - 1 Jun 2016

Keywords

Heisenberg group
Nonexistence
Nonlinear pseudo-parabolic equation
System

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10.1007/s00605-015-0823-7

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title = "Nonexistence results for pseudo-parabolic equations in the Heisenberg group",

abstract = "We derive sufficient conditions for the nonexistence of global weak solutions to the nonlinear pseudo-parabolic equation (Formula presented.), where ΔH is the Kohn–Laplace operator on the (2N + 1) -dimensional Heisenberg group H, p> 1 and f(t, ϑ) is a given function. Next, we extend this result to the case of systems. Our technique of proof is based on the test function method.",

keywords = "Heisenberg group, Nonexistence, Nonlinear pseudo-parabolic equation, System",

author = "Mohamed Jleli and Mokhtar Kirane and Bessem Samet",

note = "Funding Information: M. Jleli and B. Samet would like to extend their sincere appreciation to the Deanship of Scientific Research at King Saud University for its funding of this research through the Research Group Project No RGP-1435-034. Publisher Copyright: {\textcopyright} 2015, Springer-Verlag Wien.",

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T1 - Nonexistence results for pseudo-parabolic equations in the Heisenberg group

AU - Jleli, Mohamed

AU - Kirane, Mokhtar

AU - Samet, Bessem

N1 - Funding Information: M. Jleli and B. Samet would like to extend their sincere appreciation to the Deanship of Scientific Research at King Saud University for its funding of this research through the Research Group Project No RGP-1435-034. Publisher Copyright: © 2015, Springer-Verlag Wien.

PY - 2016/6/1

Y1 - 2016/6/1

N2 - We derive sufficient conditions for the nonexistence of global weak solutions to the nonlinear pseudo-parabolic equation (Formula presented.), where ΔH is the Kohn–Laplace operator on the (2N + 1) -dimensional Heisenberg group H, p> 1 and f(t, ϑ) is a given function. Next, we extend this result to the case of systems. Our technique of proof is based on the test function method.

AB - We derive sufficient conditions for the nonexistence of global weak solutions to the nonlinear pseudo-parabolic equation (Formula presented.), where ΔH is the Kohn–Laplace operator on the (2N + 1) -dimensional Heisenberg group H, p> 1 and f(t, ϑ) is a given function. Next, we extend this result to the case of systems. Our technique of proof is based on the test function method.

KW - Heisenberg group

KW - Nonexistence

KW - Nonlinear pseudo-parabolic equation

KW - System

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U2 - 10.1007/s00605-015-0823-7

DO - 10.1007/s00605-015-0823-7

M3 - Article

AN - SCOPUS:84944548778

SN - 0026-9255

VL - 180

SP - 255

EP - 270

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

IS - 2

ER -

Nonexistence results for pseudo-parabolic equations in the Heisenberg group

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