Formulas for generalized principal Lyapunov exponent for parabolic PDEs

Janusz  Mierczyński; Wenxian Shen

doi:10.3934/dcdss.2016048

Article Contents

2016, Volume 9, Issue 4: 1189-1199. Doi: 10.3934/dcdss.2016048

This issue Previous Article Local study of a renormalization operator for 1D maps under quasiperiodic forcing Next Article Forced linear oscillators and the dynamics of Euclidean group extensions

Formulas for generalized principal Lyapunov exponent for parabolic PDEs

Janusz Mierczyński^1, and
Wenxian Shen^2,

1.
Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, PL-50-370 Wrocław
2.
Department of Mathematics & Statistics, Auburn University, Auburn, AL 36849

Received: July 31, 2015

Revised: January 31, 2016

Published: July 2016

Abstract Related Papers Cited by

Abstract

An integral formula is given representing the generalized principal Lyapunov exponent for random linear parabolic PDEs. As an application, an upper estimate of the exponent is obtained.

Keywords:

Mathematics Subject Classification: Primary: 37H15; Secondary: 35K10, 35R60.

Citation:

Related Papers

Cited by

References

[1]	C. D. Aliprantis and K. C. Border, Infinite Dimensional Analysis. A Hitchhiker's Guide, third edition, Springer, Berlin, 2006.
[2]	J. Diestel and J. J. Uhl, Jr., Vector Measures, with a foreword by B. J. Pettis, Mathematical Surveys, No. 15, American Mathematical Society, Providence, R.I., 1977.
[3]	L. C. Evans, Partial Differential Equations, Grad. Stud. Math., 19, American Mathematical Society, Providence, R.I., 1998.
[4]	U. Krengel, Ergodic Theorems, Walter de Gruyter, Berlin, 1985.doi: 10.1515/9783110844641.
[5]	J. Mierczyński, Estimates for principal Lyapunov exponents: A survey, Nonautonomous Dynamical Systems, 1 (2014), 137-162.
[6]	J. Mierczyński and W. Shen, Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications, Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics, Chapman & Hall/CRC, Boca Raton, FL, 2008.doi: 10.1201/9781584888963.
[7]	J. Mierczyński and W. Shen, Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. I. General theory, Trans. Amer. Math. Soc., 365 (2013), 5329-5365.doi: 10.1090/S0002-9947-2013-05814-X.
[8]	J. Mierczyński and W. Shen, Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. III. Parabolic equations and delay systems, J. Dynam. Differential Equations, 28 (2016), 1039-1079.doi: 10.1007/s10884-015-9436-z.