两温度理论中的半线性热传导方程的初边值问题

Initial-boundary Value Problem of Semilinear Heat Equation Arising in Dual Temperature Theory

研究热传导的两温度理论中的半线性方程 u_t-△u_t-△u=f(u)的初边值问题,证明了当 f′(u)上方有界且满足增长条件(7)时,问题存在唯一整体广义解与整体强解,并讨论了解的渐近性质。

In this paper, we study the initial -boundary value problem of sernilinear heat equation arising in dual temperature theory u_t -Δu_t -Δu = f( u ) , prove that if f′( u ) is bounded above and satisfies growth condition (7), there will exist a unique global generalized solution and a global strong solution, are discuss also the asymptotic behavior of these solutions.