As an extension to the derivative-dependent functional variable separation approach, the approximate derivative-dependent functional variable separation approach is proposed, and it is applied to study the generalized...As an extension to the derivative-dependent functional variable separation approach, the approximate derivative-dependent functional variable separation approach is proposed, and it is applied to study the generalized diffusion equations with perturbation. Complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is obtained. As a result, the corresponding approximate derivative-dependent functional separable solutions to some resulting perturbed equations are derived by way of examples.展开更多
The transport behavior of free boundary value problems for a class ofgeneralized diffusion equations was studied. Suitable similarity transformations were used toconvert the problems into a class of singular nonlinear...The transport behavior of free boundary value problems for a class ofgeneralized diffusion equations was studied. Suitable similarity transformations were used toconvert the problems into a class of singular nonlinear two-point boundary value problems andsimilarity solutions were numerical presented for different representations of heat conductionfunction, convection function, heat flux function, and power law parameters by utilizing theshooting technique. The results revealed the flux transfer mechanism and the character as well asthe effects of parameters on the solutions.展开更多
In this paper, we use the Mittag-Leffler addition formula to solve the Green function of generalized time fractional diffusion equation in the whole plane and prove the convergence of the Green function.
The author demonstrate that the two-point boundary value problemhas a solution (A,P(8)), where III is the smallest parameter, under the minimal stringent resstrictions oil f(8), by applying the shooting and regularisa...The author demonstrate that the two-point boundary value problemhas a solution (A,P(8)), where III is the smallest parameter, under the minimal stringent resstrictions oil f(8), by applying the shooting and regularisation methods. In a classic paper)Kolmogorov et. al. studied in 1937 a problem which can be converted into a special case of theabove problem.The author also use the solutioll (A, p(8)) to construct a weak travelling wave front solutionu(x, t) = y((), (= x -- Ct, C = AN/(N + 1), of the generalized diffusion equation with reactionO { 1 O.IN￣1 OUI onde L k(u) i ox: &) ￣ & = g(u),where N > 0, k(8) > 0 a.e. on [0, 1], and f(s):= ac i: g(t)kl/N(t)dt is absolutely continuouson [0, 11, while y(() is increasing and absolutely continuous on (--co, +co) and(k(y(())ly,(OI'), = g(y(()) -- Cy'(f) a.e. on (--co, +co),y(￣oo) ￣ 0, y(+oo) ￣ 1.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.10671156the Natural Science Foundation of Shaanxi Province of China under Grant No.SJ08A05
文摘As an extension to the derivative-dependent functional variable separation approach, the approximate derivative-dependent functional variable separation approach is proposed, and it is applied to study the generalized diffusion equations with perturbation. Complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is obtained. As a result, the corresponding approximate derivative-dependent functional separable solutions to some resulting perturbed equations are derived by way of examples.
基金This work was financially supported by the Cross-Century Talents Projects of Educational Ministry of China and the 973 Key Item (No. G1998061510).]
文摘The transport behavior of free boundary value problems for a class ofgeneralized diffusion equations was studied. Suitable similarity transformations were used toconvert the problems into a class of singular nonlinear two-point boundary value problems andsimilarity solutions were numerical presented for different representations of heat conductionfunction, convection function, heat flux function, and power law parameters by utilizing theshooting technique. The results revealed the flux transfer mechanism and the character as well asthe effects of parameters on the solutions.
文摘In this paper, we use the Mittag-Leffler addition formula to solve the Green function of generalized time fractional diffusion equation in the whole plane and prove the convergence of the Green function.
文摘The author demonstrate that the two-point boundary value problemhas a solution (A,P(8)), where III is the smallest parameter, under the minimal stringent resstrictions oil f(8), by applying the shooting and regularisation methods. In a classic paper)Kolmogorov et. al. studied in 1937 a problem which can be converted into a special case of theabove problem.The author also use the solutioll (A, p(8)) to construct a weak travelling wave front solutionu(x, t) = y((), (= x -- Ct, C = AN/(N + 1), of the generalized diffusion equation with reactionO { 1 O.IN￣1 OUI onde L k(u) i ox: &) ￣ & = g(u),where N > 0, k(8) > 0 a.e. on [0, 1], and f(s):= ac i: g(t)kl/N(t)dt is absolutely continuouson [0, 11, while y(() is increasing and absolutely continuous on (--co, +co) and(k(y(())ly,(OI'), = g(y(()) -- Cy'(f) a.e. on (--co, +co),y(￣oo) ￣ 0, y(+oo) ￣ 1.
