论文信息 - A Lyapunov functional for the evolution of solutions to the porous medium equation to self‐similarity. I - 字舞流文

A Lyapunov functional for the evolution of solutions to the porous medium equation to self‐similarity. I

We employ the transformation properties and the integral invariants of the porous medium equation in m dimensions to construct a Lyapunov functional which characterizes the evolution of the profile to its self‐similar solution.

William I. Newman | W. I. Newman

[1] J. Berryman. Evolution of a stable profile for a class of nonlinear diffusion equations. III. Slow diffusion on the line , 1980 .

[2] G. I. Barenblatt,et al. Self-Similar Solutions as Intermediate Asymptotics , 1972 .

[3] James Ralston,et al. A Lyapunov functional for the evolution of solutions to the porous medium equation to self‐similarity. II , 1984 .

[4] R. E. Pattle. DIFFUSION FROM AN INSTANTANEOUS POINT SOURCE WITH A CONCENTRATION-DEPENDENT COEFFICIENT , 1959 .

[5] S. Kamenomostskaya,et al. The asymptotic behaviour of the solution of the filtration equation , 1973 .

[6] G. I. Barenblatt,et al. Similarity, Self-Similarity and Intermediate Asymptotics , 1979 .

[7] J. Cole,et al. Similarity methods for differential equations , 1974 .

[8] W. I. Newman. The long-time behavior of the solution to a non-linear diffusion problem in population genetics and combustion , 1983 .