Nonexistence results for higher order pseudo‐parabolic equations in the Heisenberg group | Zendy

Alsaedi Ahmed | Zendy; Ahmad Bashir | Zendy; Kirane Mokhtar | Zendy; AlYami Maryem | Zendy

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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.

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