scholarly journals Decay mild solutions of the nonlocal Cauchy problem for second order evolution equations with memory

2016 ◽  
pp. 1-15 ◽  
Author(s):  
Vu Trong Luong
Keyword(s):  
Cauchy Problem ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Second Order ◽  
Nonlocal Cauchy Problem ◽  
With Memory

scholarly journals Decay estimates for second order evolution equations with memory

2008 ◽  
Vol 254 (5) ◽  
pp. 1342-1372 ◽  
Author(s):  
Fatiha Alabau-Boussouira ◽  
Piermarco Cannarsa ◽  
Daniela Sforza
Keyword(s):  
Evolution Equations ◽  
Second Order ◽  
Decay Estimates ◽  
With Memory

scholarly journals Fractional Measure-dependent Nonlinear Second-order Stochastic Evolution Equations with Poisson Jumps

2018 ◽  
Vol 5 (1) ◽  
pp. 59-75 ◽  
Author(s):  
Mark A. McKibben ◽  
Micah Webster
Keyword(s):  
Evolution Equations ◽  
Mild Solutions ◽  
Stability Result ◽  
Growth Conditions ◽  
Second Order ◽  
Probability Measures ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Poisson Jumps ◽  
Fractional Measure

Abstract This paper focuses on a nonlinear second-order stochastic evolution equations driven by a fractional Brownian motion (fBm) with Poisson jumps and which is dependent upon a family of probability measures. The global existence of mild solutions is established under various growth conditions, and a related stability result is discussed. An example is presented to illustrate the applicability of the theory.

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