Volterra series for solving weakly non-linear partial differential equations: Application to a dissipative Burgers' equation

International Journal of Control

Volumn 77, Issue 12, 2004, Pages 1071-1082

  Hélie, Thomas ^a   Hasler, Martin ^b  

^a UNIV PARIS SUD   (France)

^b EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC WAVE PROPAGATION; BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; HARMONIC ANALYSIS; LAPLACE TRANSFORMS; MATHEMATICAL MODELS; NONLINEAR EQUATIONS;

HARMONIC BALANCE METHOD; LAPLACE DOMAIN; VISCOTHERMAL LOSSES; VOLTERRA SYSTEM;

MUSICAL INSTRUMENTS;

EID: 7544235262     PISSN: 00207179     EISSN: None     Source Type: Journal    
DOI: 10.1080/002071704200024365     Document Type: Article

References (8)

1. ABRAMOWITZ, M., and STEGUN, I. A., 1970, Handbook of Mathematical Functions (New York: Dover).
2. BOYD, S. P., 1985, Volterra series: Engineering fundamentals. PhD thesis, Harvard University.
3. HASLER, M., 1999, Phénomènes non linéaires, École Polytechnique Fédérale de Lausanne.
4. MENGUY, L., and GILBERT, J., 2000, Weakly non-linear gas oscillations in air-filled tubes: solutions and experiment. Acta Acusitica, 86, 798-810.
5. NAKHLA, M. S., and VLACH, J., 1976, A piecewise harmonic balance technique for determination of periodic response of nonlinear systems. IEEE Transactions on Circuit Theory, 23, 85-91.
6. RUGH, W. J., 1981, Nonlinear System Theory, The Volterra/Wiener Approach (Baltimore: The Johns Hopkins University Press).
7. SCHELKUNOFF, S. A., 1945, Electromagnetic Waves (New York: Von Nostrand).
8. STAFFANS, O. J., 1994, Well-posedness and stabilizability of a viscoelastic equation in energy space. Transactions of the American Mathematical Society, 345, 527-575.