The Kontorovich-Lebedev transform and its associated pseudodifferential operator

2017 ◽  
Vol 41 (1) ◽  
pp. 46-57
Author(s):  
Akhilesh Prasad ◽  
Upain Kumar Mandal
Keyword(s):  
Pseudodifferential Operator

scholarly journals The problem of the first return attached to a pseudodifferential operator in dimension 3

2015 ◽  
pp. 107-119 ◽  
Author(s):  
Oscar Casas Sánchez ◽  
Jeanneth Galeano Peñaloza ◽  
John Rodríguez Vega
Keyword(s):  
Pseudodifferential Operator

scholarly journals Asymptotics for the Ostrovsky-Hunter Equation in the Critical Case

2017 ◽  
Vol 2017 ◽  
pp. 1-21
Author(s):  
Fernando Bernal-Vílchis ◽  
Nakao Hayashi ◽  
Pavel I. Naumkin
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Pseudodifferential Operator ◽  
Critical Case ◽  
Large Time ◽  
Asymptotic Behavior Of Solutions ◽  
The Cauchy Problem ◽  
Time Existence ◽  
Time Asymptotic Behavior

We consider the Cauchy problem for the Ostrovsky-Hunter equation ∂x∂tu-b/3∂x3u-∂xKu3=au, t,x∈R2,  u0,x=u0x, x∈R, where ab>0. Define ξ0=27a/b1/4. Suppose that K is a pseudodifferential operator with a symbol K^ξ such that K^±ξ0=0, Im K^ξ=0, and K^ξ≤C. For example, we can take K^ξ=ξ2-ξ02/ξ2+1. We prove the global in time existence and the large time asymptotic behavior of solutions.

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