tailieunhanh - Handbook of mathematics for engineers and scienteists part 203

Handbook of mathematics for engineers and scienteists part 203. Tài liệu toán học quốc tế để phục vụ cho các bạn tham khảo, tài liệu bằng tiếng anh rất hữu ích cho mọi người. | 1382 Systems of Partial Differential Equations Solution Um Pm t Fn t e xi . Xn t i g t pi _. . n 1 dt m 1 . n - 1 L J Fn t -I Un Fn t 0x1 . Xn t i F1 . F dt L J Fn t -I Fn t exp fn t F1 . Fn-1 d where the functions Fm . m t are described by the nonlinear system of first-order ordinary differential equations m Fm fm t F1 . . . Fn-1 fn t 1 . n-1 L m 1 . n 1 and the function 0 0 x1 . xn t satisfies the linear equation I . n 3. L um ukfmk t -- d k 1 V Un un-1 un m 1 . n. Here the system involves n2 arbitrary functions fmk fmk t z1 . zn-1 that depend on n arguments L is an arbitrary linear differential operator with respect to the spatial variables x1 . xn of any order in derivatives whose coefficients can be dependent on x1 . xn t. It is assumed that L const 0. Solution um xi . xn t Vm t F t O xi . xn t F t exp n 2 Vk t fnk t V1 . Vn-1 dt k 1 m 1 . n Vn t 1 where the functions Fm Fm t are described by the nonlinear system of first-order ordinary differential equations nn Fm Fkfmk t 1 . n-1 rm k fnk t 1 . n-1 m 1 . n 1 and the function 0 0 X1 . Xn t satisfies the linear equation d0 L 0l References for Chapter T10 Barannyk T. Symmetry and exact solutions for systems of nonlinear reaction-diffusion equations Proc. of Inst. of Mathematics of NAS of Ukraine Vol. 43 Part 1 pp. 80-85 2002. Barannyk T. A. and Nikitin A. G. Proc. of Inst. of Mathematics of NAS of Ukraine Vol. 50 Part 1 pp. 34-39 2004. Cherniha R. and King J. R. Lie symmetries of nonlinear multidimensional reaction-diffusion systems I J. Phys. A Math. Gen. Vol. 33 pp. 267-282 7839-7841 2000. References for Chapter T10 1383 Cherniha R. and King J. R. Lie symmetries of nonlinear multidimensional reaction-diffusion systems II J. Phys. A Math. Gen. Vol. 36 pp. 405-425 2003. Nikitin A. G. Group classification of systems of non-linear reaction-diffusion equations with general diffusion matrix. II. Diagonal diffusion matrix From Website a service of automated e-print archives of articles http abs .