scholarly journals Stepanov-like pseudo almost automorphic solution to a parabolic evolution equation

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Desheng Ji ◽  
Yueming Lu
Keyword(s):  
Evolution Equation ◽  
Parabolic Evolution Equation ◽  
Almost Automorphic ◽  
Pseudo Almost Automorphic ◽  
Pseudo Almost Automorphic Solution

scholarly journals Existence and Uniqueness of Pseudo Almost Automorphic Mild Solutions to Some Classes of Partial Hyperbolic Evolution Equations

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Zhanrong Hu ◽  
Zhen Jin
Keyword(s):  
Evolution Equation ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Existence And Uniqueness Theorem ◽  
Abstract Result ◽  
Almost Automorphic ◽  
Pseudo Almost Automorphic

We will establish an existence and uniqueness theorem of pseudo almost automorphic mild solutions to the following partial hyperbolic evolution equation(d/dt)[u(t)+f(t,Bu(t))]=Au(t)+g(t,Cu(t)),  t∈ℝ,under some assumptions. To illustrate our abstract result, a concrete example is given.

scholarly journals Pseudo almost automorphic solutions of class r in α-norm under the light of measure theory

2020 ◽  
Vol 7 (1) ◽  
pp. 81-101
Author(s):  
Issa Zabsonre ◽  
Djendode Mbainadji
Keyword(s):  
Phase Space ◽  
Spectral Decomposition ◽  
Measure Theory ◽  
New Approach ◽  
Almost Automorphic ◽  
Almost Automorphic Functions ◽  
Pseudo Almost Automorphic ◽  
Automorphic Functions

AbstractUsing the spectral decomposition of the phase space developed in Adimy and co-authors, we present a new approach to study weighted pseudo almost automorphic functions in the α-norm using the measure theory.

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