Nội dung được dịch bởi AI, chỉ mang tính chất tham khảo
Một số phương trình phi tuyến có thể rút gọn thành phương trình loại khuếch tán
Tóm tắt
Vấn đề rút gọn một hệ phương trình vi phân parabol cấp hai phi tuyến thành các phương trình loại khuếch tán được xem xét. Một thuật toán giải quyết hiệu quả cho vấn đề này được đề xuất trong trường hợp không đồng nhất.
Từ khóa
Tài liệu tham khảo
M. V. Pavlov, S. I. Svinolupov, and R. A. Sharipov,Funct. Anal. Appl.,30, 15–22 (1996); “An invariant criterion for the hydrodynamic integrability of hydrodynamic-type equations [in Russian],” in:Integrability in Dynamic Systems (L. A. Kalyakin, ed.), Inst. Math. Comp. Center Russ. Acad. Sci., Ufa (1994), pp. 27–48; Preprint solv-int/9407003 (1994).
E. V. Ferapontov and R. A. Sharipov,Theor. Math. Phys.,108, 937–952 (1996); Preprint solv-int/9607003 (1996).
V. V. Dmitrieva and R. A. Sharipov, “On the point transformations for the second-order differential equations,” Preprint solv-int/9703003 (1997).
R. A. Sharipov, “On the point transformations for the equationy″=P+3Qy′+3Ry″ 2+Sy′3,” Preprint solv-int/9706003 (1997).
O. N. Mikhailov and R. A. Sharipov, “On the point expansion for the certain class of differential equations of the second order,” Preprint solv-int/9712001 (1997).
R. A. Sharipov, “Effective procedure of point classification for the equationsy″=P+3Qy′+3Ry′ 2+Sy′3,” Preprint Math. DG/9802027 (1998).
G. W. Bluman and K. Kumei,Symmetries and Differential Equations, Springer, Berlin (1989).
P. Broadbridge and I. White,Water Resources Res.,24, 145–154 (1987).
D. A. De Vries,Trans. Am. Geophys. Union,39, 909–916 (1958).
M. P. Edwards and P. Broadbridge,J. Phys. A,27, 5455–5465 (1994).
R. D. Jackson,Proc. Am. Soil Sci. Soc.,37, 505–509 (1973).
W. A. Jury, J. Letey, and L. H. Stolzy, “Flow of water and energy under desert conditions,” in:Water in Desert, Ecosystems (D. D. Evans and J. L. Thames, eds.). Dowden, Hutchinson, and Ross, Stroudsburg, PA (1981), pp. 92–113.
J. H. Knight and J. R. Philip,J. Eng. Math.,8, 219–227 (1974).
M. R. Myerscough and J. D. Murray,Bull. Math. Biol.,54, No. 1, 77–94 (1992).
L. V. Ovsyannikov,Dokl. Akad. Nauk SSSR,123, 492–495 (1959).
J. R. Philip, “Quasi-analytic and analytic approaches to unsaturated flow,” in:Flow and Transport in the Natural Environment: Advances and Applications (W. L. Steffen and O. T. Denmead, eds.), Springer, Berlin (1988), pp. 30–48.
J. R. Philip and D. A. De Vries,Trans. Am. Geophys. Union,38, 222–232 (1957).
C. W. Rose,Aust. J. Soil Res.,6, 31–44 (1968).
R. Shepherd and R. J. Wiltshire,Trans. Porous Media,20, 281–304 (1995).
R. Shepherd and R. J. Wiltshire,IMA J. Appl. Math.,56, 277–287 (1996).
J. A. SherrattBull. Math. Biol.,56, No. 1, 129–146 (1994).
C. Sophocleous,J. Phys. A,29, 6951–6959 (1996).
R. J. Wiltshire,J. Phys. A,27, 7821–7829 (1994).
V. A. Baikov, A. V. Gladkov, and R. J. Wiltshire,J. Phys. A,31, 7483–7499 (1998).
A. V. Mikhailov and A. B. Shabat, “Integrability conditions for the system of two equations of the formu t=A(u)uxx+F(u, ux),” Preprint, Inst. Theor. Phys, Chernogolovka (1985).
S. I. Svinolupov, “On multified analogues of the Burgers equation [in Russian],” Report, for the Presidium, Bashkir Div. Russ. Acad. Sci., Ufa (1987).
S. I. Svinolupov,Phys. Lett. A,135, No. 1, 32 (1989).
S. I. Svinolupov and I. T. Khabibullin,Math. Notes,60, 671–680 (1996).
I. Z. Golubchik and V. V. Sokolov,Funct. Anal. Appl.,30, 275–277 (1996).
I. Z. Golubchik and V. V. Sokolov,Theor. Math. Phys.,112, 1097–1103 (1997).
A. I. Kostrikin,Introduction to Algebra [in Russian], Nauka, Moscow (1977); English transl., Springer, New York (1982).
S. Lang,Algebra, Addison-Wesley, Reading, MA (1965).
R. A. Sharipov,A Course in Linear Algebra and Multidimensional Geometry [in Russian], Bashkir State Univ. Press, Ufa (1996).