scholarly journals Lumpability of linear evolution Equations in Banach spaces

2017 ◽  
Vol 6 (1) ◽  
pp. 15-34 ◽  
Author(s):  
Fatihcan M. Atay ◽  
◽  
Lavinia Roncoroni ◽  
Keyword(s):  
Banach Spaces ◽  
Evolution Equations ◽  
Linear Evolution ◽  
Linear Evolution Equations

scholarly journals Ulam-Hyers stability and exponentially stable evolution equations in Banach spaces

2021 ◽  
Vol 37 (2) ◽  
pp. 339-344
Author(s):  
ADRIANA BUICĂ
Keyword(s):  
Banach Spaces ◽  
Evolution Equations ◽  
Nonlinear Term ◽  
Lipschitz Constant ◽  
Special Relation ◽  
Linear Evolution ◽  
Exponentially Stable ◽  
Linear Evolution Equations

We show that uniformly exponentially stable abstract linear evolution equations are Ulam-Hyers stable on [a,\infty). Moreover, we prove that this property is maintained when perturbing this type of equations with a nonlinear term having a small Lipschitz constant. These results complement the literature on Ulam-Hyers stability, a special relation having with some works of I. A. Rus.

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