Pardomuan Sitompul, Yudi Soeharyadi
In this paper we consider an IBVP semilinear diffusion equation of the form ut=Duxx+sin(2pu) (x,t)[0,1]×(0,8),ut(0,t)=ut(1,t)=0 t>0,u(0,x)=?(x) x[0,1]. We show that energy of the solution, i.e. the L2 - norm of the gradient, decays with an upper bound estimate which depends on the diffusion coefficient. For a particular initial data which is monotone and symmetric, the solution remains symmetric. Furthermore, with a particular symmetry, the energy of the solution converges to a constant C > 0, in the long run. © 2024 Author(s).
Universitas Negeri Medan, Medan, Indonesia; Institut Teknologi Bandung, Bandung, Indonesia
