Article Contents
Article Contents

# On the oscillation behavior of solutions to the one-dimensional heat equation

• We study the oscillation behavior of solutions to the one-dimensional heat equation and give some interesting examples. We also demonstrate a simple ODE method to find explicit solutions of the heat equation with certain particular initial conditions.

Mathematics Subject Classification: 35K05, 35K15.

 Citation:

•  [1] P. Collet and J. -P. Eckmann, Space-time behavior in problems of hydrodynamic type: A case study, Nonlinearity, 5 (1992), 1265-1302.  doi: 10.1088/0951-7715/5/6/004. [2] S. D. Eidel'man, Parabolic System, North-Holland, Amsterdam, 1969. [3] S. Kamin, On stabilization of solutions of the Cauchy problem for parabolic equations, Proc. Roy. Soc. Edinburgh Sect. A, 76/77 (1976), 43-53.  doi: 10.1017/S0308210500019478. [4] M. Nara and M. Taniguchi, The condition on the stability of stationary lines in a curvature flow in the whole plane, J. Diff. Eq., 237 (2007), 61-76.  doi: 10.1016/j.jde.2007.02.012. [5] W.-M. Ni, The Mathematics of Diffusion, CBMS-NSF Regional Conference Series in Applied Mathematics, v. 82, SIAM, 2011. doi: 10.1137/1.9781611971972. [6] V. D. Repnikov and S. D. Eidel'man, A new proof of the theorem on the stabilization of the solution of the Cauchy problem for the heat equation, Math. USSR Sb., 2 (1967), 135-139.  doi: 10.1070/SM1967v002n01ABEH002328.