Asymptotic Stability for an Axis-Symmetric Ohmic Heating Model in Thermal Electricity

[摘要] The asymptotic behavior of the solution for the Dirichlet problem of the parabolic equation with nonlocal termut=urr+ur/r+f(u)/(a+2πb∫01‍f(u)rdr)2,for  00,u1,t=u′(0,t)=0,for  t>0,  ur,0=u0r,  for  0≤r≤1. The model prescribes the dimensionless temperature when the electric current flows through two conductors, subject to a fixed potential difference. One of the electrical resistivity of the axis-symmetric conductor depends on the temperature and the other one remains constant. The main results show that the temperature remains uniformly bounded for the generally decreasing functionf(s), and the global solution of the problem converges asymptotically to the unique equilibrium.

[学科分类] 应用数学