On a Diffusion Equation with a Damping Term

DOI：10.16205/j.cnki.cama.2021.0016

 作者 单位 詹华税 厦门理工学院应用数学学院, 福建 厦门 361024. 袁洪君 吉林大学数学学院, 长春 130012.

讨论了该方程的初边值问题解的存在性, 其中$\alpha>0$, \$q

The authors study diffusion equation with a damping term ?u ?t = div(ρα|?u|p?2?u) ? a(x)|?u|q ,where α > 0, q < p, ρ(x) = dist(x, ??) is the distance function from the boundary ??, a(x)is a nonnegative bounded function. By the parabolic regularized method, the existence of the weak solution is obtained. By choosing a suitable test function, the uniqueness of the weak solution is proved without any boundary value condition.