grandes-ecoles 2022 Q23

grandes-ecoles · France · mines-ponts-maths2__mp Second order differential equations Qualitative and asymptotic analysis of solutions

In all that follows, $\mathbf{K = C}$. We set $E = \mathbf{C}^n$. We are given $A \in \mathcal{M}_n(\mathbf{C})$. We set $\alpha = \max_{\lambda \in \operatorname{Sp}(A)} \operatorname{Re}(\lambda)$.
$\mathbf{23}$ ▷ Study the converse of question 19): that is, show that if $\alpha < 0$ then $\lim_{t \rightarrow +\infty} f_A(t) = 0_n$.

In all that follows, $\mathbf{K = C}$. We set $E = \mathbf{C}^n$. We are given $A \in \mathcal{M}_n(\mathbf{C})$. We set $\alpha = \max_{\lambda \in \operatorname{Sp}(A)} \operatorname{Re}(\lambda)$.

$\mathbf{23}$ ▷ Study the converse of question 19): that is, show that if $\alpha < 0$ then $\lim_{t \rightarrow +\infty} f_A(t) = 0_n$.

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q24 Q25 Q26