scholarly journals Square-mean asymptotically almost periodic solutions of second order nonautonomous stochastic evolution equations

2021 ◽  
Vol 6 (5) ◽  
pp. 5040-5052
Author(s):  
Jinghuai Liu ◽  
◽  
Litao Zhang
Keyword(s):  
Periodic Solutions ◽  
Evolution Equations ◽  
Second Order ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Asymptotically Almost Periodic

ALMOST PERIODIC SOLUTIONS TO STOCHASTIC EVOLUTION EQUATIONS ON BANACH SPACES

2013 ◽  
Vol 13 (03) ◽  
pp. 1250027 ◽  
Author(s):  
P. CREWE
Keyword(s):  
Banach Space ◽  
Periodic Solutions ◽  
Banach Spaces ◽  
Evolution Equations ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Stochastic Integration ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Semigroup Generator

We prove the existence of almost periodic solutions to a class of abstract stochastic evolution equations on a Banach space E, [Formula: see text] Both autonomous (A is a C0-semigroup generator) and non-autonomous (A(t) satisfies conditions of Acquistapace–Terreni and generates a strongly continuous evolution family) cases are studied. Results are based on the theory of stochastic integration on Banach spaces of van Neerven and Weis and R-boundedness estimates for semigroups and evolution families due to Hytönen and Veraar. An example is given for a non-autonomous second order boundary value problem on a domain in ℝd.

scholarly journals Asymptotically almost periodic solutions of fractional evolution equations

2021 ◽  
Vol 8 (3) ◽  
pp. 475-483
Author(s):  
Duc Huy Nguyen ◽  
◽  
Trong Luong Vu ◽  
Keyword(s):  
Periodic Solutions ◽  
Evolution Equations ◽  
Initial Boundary ◽  
Asymptotic Behavior Of Solutions ◽  
Operator Family ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Fractional Evolution Equations ◽  
Exponentially Stable ◽  
Asymptotically Almost Periodic

We study the asymptotic behavior of solutions of nonlinear fractional evolution equations in Banach spaces. Asymptotically almost periodic solutions on half line are obtained by establishing a sharp estimate on the resolvent operator family of evolution equations. In particular, when the semigroup generated by A is exponentially stable then the conditions of the existence asymptotically almost periodic solutions is satisfied. An application to a fractional partial differential equation with initial boundary condition is also considered.

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