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Lie Symmetries and Criticality of Semilinear Differential Systems
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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Lie Symmetries and Criticality of Semilinear Differential Systems
Інший ID:
2000 Mathematics Subject Classification: 35J50; 35J20; 35J60; 35L70
Посилання:
Lie Symmetries and Criticality of Semilinear Differential Systems / Y. Bozhkov, E. Mitidieri // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 39 назв. — англ.
Підтримка:
We wish to thank the referees for their useful suggestions. Yuri Bozhkov is grateful to the Organizers of the 7th International Conference “Symmetry in Nonlinear Mathematical Physics”, June 24–30 2007, Kyiv, Ukraine, for having given him the opportunity to present a talk on this subject. He would also like to thank FAPESP, CNPq and FAEPEX-UNICAMP, Brasil, as well as ICTP, Trieste, Italy, for financial support. Enzo Mitidieri acknowledges the support of INTAS-05-100000B-792.
Дата:
2007
Переглядів:
491
Завантажень:
245
Анотація:
We discuss the notion of criticality of semilinear differential equations and systems, its relations to scaling transformations and the Noether approach to Pokhozhaev's identities. For this purpose we propose a definition for criticality based on the S. Lie symmetry theory. We show that this definition is compatible with the well-known notion of critical exponent by considering various examples. We also review some related recent papers.
