In this paper, we deal with weakly coupled elliptic systems A with unbounded coefficients. We prove the existence and characterize all the systems of invariant measures for the semigroup (T(t))(t >= 0) associated with A in C-b(R-d; R-m). We also show some relevant properties of the extension of (T(t))(t >= 0) to the L-P-spaces related to systems of invariant measures. Finally, we study the asymptotic behaviour of (T(t))(t >= 0) as t tends to +infinity.
Addona, D., Angiuli, L., Lorenzi, L. (2019). On Invariant Measures Associated with Weakly Coupled Systems of Kolmogorov Equations. ADVANCES IN DIFFERENTIAL EQUATIONS, 24(3-4), 137-184.
On Invariant Measures Associated with Weakly Coupled Systems of Kolmogorov Equations
Addona, D
;
2019
Abstract
In this paper, we deal with weakly coupled elliptic systems A with unbounded coefficients. We prove the existence and characterize all the systems of invariant measures for the semigroup (T(t))(t >= 0) associated with A in C-b(R-d; R-m). We also show some relevant properties of the extension of (T(t))(t >= 0) to the L-P-spaces related to systems of invariant measures. Finally, we study the asymptotic behaviour of (T(t))(t >= 0) as t tends to +infinity.
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