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Nonexistence results for higher order pseudo‐parabolic equations in the Heisenberg group
Author(s) -
Alsaedi Ahmed,
Ahmad Bashir,
Kirane Mokhtar,
AlYami Maryem
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4052
Subject(s) - mathematics , heisenberg group , operator (biology) , order (exchange) , laplace transform , group (periodic table) , nonlinear system , mathematical analysis , mathematical physics , pure mathematics , physics , quantum mechanics , biochemistry , chemistry , finance , repressor , transcription factor , economics , gene
Sufficient conditions are obtained for the nonexistence of solutions to the nonlinear higher order pseudo‐parabolic equationu t + ( − Δ H ) mu t + ( − Δ H ) m u = | u | p , ( η , t ) ∈ H × ( 0 , ∞ ) ,whereΔ His the Kohn‐Laplace operator on the (2 N + 1)‐dimensional Heisenberg group H , m ≥1, p > 1. Then, this result is extended to the case of a 2 × 2‐system of the same type. Our technique of proof is based on judicious choices of the test functions in the weak formulation of the sought solutions. Copyright © 2016 John Wiley & Sons, Ltd.