两个具有Hysteresis的发展方程

摘要

Study two develop equations with hysteresis:rnutt-Δu+F(u)=f,rnut-(F(ux))x=f.rnBy introducing inverse of hysteresis operator,it is proved that the existence and uniqueness of classical solutions of one-dimension initial value problem and weak solution of multi-dimension initial boundary problem to the first equation,the existence of smooth strong solution of one-dimension initial boundary problem to the second equation.%研究如下两个具有Hysteresis的发展方程:rnutt-Δu+F(u)=f,rnut-(F(ux))x=f.rn通过引进Hysteresis算子的逆,证明了第一个方程一维初值问题古典解和多维初边值问题强解的存在惟一性以及第二个方程一维初边值问题光滑强解的存在性.