XUSUSIY HOSILALI CHIZIQLI BO‘LMAGAN DIFFERENSIAL TENGLAMALARNING AVTOMODEL VA UMUMLASHGAN AVTOMODEL YECHIMI
Ключевые слова:
автомодельное решение, нелинейные уравнения, диффузия.Аннотация
В статье рассматриваются автомодельные и обобщѐнные автомодельные решения нелинейных дифференциальных уравнений в частных производных. Показана возможность сведения уравнений к обыкновенным дифференциальным уравнениям.
Библиографические ссылки
Barenblatt G.I. Scaling, Self-Similarity, and Intermediate Asymptotics. Cambridge University Press, 1996. – 12–25-betlar (avtomodel va o'z-o'ziga o'xshashlik tushunchasi) – 67–82-betlar (diffuziya tenglamasi uchun avtomodel yechimlar)
Ovsyannikov L.V. Group Analysis of Differential Equations. Academic Press, 1982. – 31–44-betlar (masshtablash va invariant o'zgaruvchilar) – 98–115-betlar (xususiy hosilali tenglamalar uchun simmetriya usullari)
Polyanin A.D., Zaitsev V.F. Handbook of Nonlinear Partial Differential Equations. CRC Press, 2012. – 145–168-betlar (nolinear diffuziya tenglamalari) – 312–328-betlar (Burgers tenglamasi va aniq yechimlar)
Whitham G.B. Linear and Nonlinear Waves. Wiley, 1999. – 201–220-betlar (nolinear to'lqinlar va tarqalish) – 245–260-betlar (zarba va yumshatilgan zarba to'lqinlar)
Olver P.J. Applications of Lie Groups to Differential Equations. Springer, 2000. – 89–104-betlar (masshtablash simmetriyasi) – 181–195 betlar (avtomodel yechimlarni qurish)
Zeldovich Ya.B., Raizer Yu.P. Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena. Academic Press, 1966. – 52–70-betlar (zarba to'lqinlarining fizik modeli) – 134–150-betlar (nolinear gidrodinamik jarayonlar)
Bluman G.W., Kumei S. Symmetries and Differential Equations. Springer, 1989. – 23–39-betlar (Lie simmetriyalar asoslari) – 117–132-betlar (xususiy hosilali tenglamalar uchun invariant yechimlar)
Debnath L. Nonlinear Partial Differential Equations for Scientists and Engineers. Birkhäuser, 2012. – 56–74-betlar (nolinear tenglamalarning umumiy xususiyatlari) – 210–225-betlar (diffuziya va konveksiya modellari)
Samarskii A.A., Galaktionov V.A., Kurdyumov S.P. Blow-up in Quasilinear Parabolic Equations. Walter de Gruyter, 1995. – 14–28-betlar (parabolik tenglamalarning umumiy nazariyasi) – 95–110-betlar (avtomodel tipdagi yechimlar)
Lie S. Theory of Transformation Groups. Chelsea Publishing, 1970. – 61–78-betlar (o'lcham va masshtablash o'zgarishlari) – 140–155-betlar (invariant yechimlar nazariyasi)
