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October  2013, 18(8): 2143-2149. doi: 10.3934/dcdsb.2013.18.2143

A note on global asymptotic stability of nonautonomous master equations

 1 Lehrstuhl A für Mathematik, RWTH Aachen, D-52056 Aachen, Germany 2 Lehrstuhl A für Mathematik, RWTH Aachen, 52056 Aachen

Received  March 2013 Revised  May 2013 Published  July 2013

We present sufficient conditions to either preclude or guarantee global asymptotic stability of linear differential equations for time-dependent $\mathbb W$-matrices. These conditions are concerned with integrability or non-integrability of the matrix entries. The proofs employ differential inequalities.
Citation: Christian Lax, Sebastian Walcher. A note on global asymptotic stability of nonautonomous master equations. Discrete & Continuous Dynamical Systems - B, 2013, 18 (8) : 2143-2149. doi: 10.3934/dcdsb.2013.18.2143
References:
 [1] A. Berman and R. J. Plemmons, "Nonnegative Matrices in the Mathematical Sciences," Computer Science and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1979.  Google Scholar [2] B. A. Earnshaw and J. P. Keener, Global asymptotic stability of solutions of nonautonomous master equations, SIAM J. Applied Dynamical Systems, 9 (2010), 220-237. doi: 10.1137/090763421.  Google Scholar [3] N. G. van Kampen, "Stochastic Processes in Physics and Chemistry," Lecture Notes in Mathematics, 888, North-Holland Publishing Co., Amsterdam-New York, 1981.  Google Scholar [4] W. Walter, "Gewöhnliche Differentialgleichungen," 7. Aufl., Springer-Verlag, Berlin, 2000. Google Scholar

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References:
 [1] A. Berman and R. J. Plemmons, "Nonnegative Matrices in the Mathematical Sciences," Computer Science and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1979.  Google Scholar [2] B. A. Earnshaw and J. P. Keener, Global asymptotic stability of solutions of nonautonomous master equations, SIAM J. Applied Dynamical Systems, 9 (2010), 220-237. doi: 10.1137/090763421.  Google Scholar [3] N. G. van Kampen, "Stochastic Processes in Physics and Chemistry," Lecture Notes in Mathematics, 888, North-Holland Publishing Co., Amsterdam-New York, 1981.  Google Scholar [4] W. Walter, "Gewöhnliche Differentialgleichungen," 7. Aufl., Springer-Verlag, Berlin, 2000. Google Scholar
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