关于固体燃烧的一类双自由边界问题

The Free Boundary Problem with Two Boundaries on Combustion of Solid

研究双自由边界边问题:u_(1t)=u_(1xx),D_r={(x,t) |r(t)<x<s(t),0<t≤T},u_1(x,0)=φ_t(x),r(0)=a<x<b=s(0),u_(1x)(s(t),t)=-[γ(t)+u_1(s(t),t)]s(t),0<t≤T,u_(1x)(r(t),t)=-[γ(t)+u_1(r(t),t)]r(t),u_2(s(t),t)=[μ(t)-u_2(s(t),t)]s(t),u_(2x)(r(t),t)=[μ(t)-u_2(r(t),t)]r(t),0<t≤T,s(t)=v_1(U_2(s(t),t))exp{-δ/u_2s(t),t)}.F_1(u_1(s(t),t),0<t≤T,r(t)=v_2(u_2(r(t),t))exp{-δ/u_2(r(t),t)}F_2(u_1(r(t),t))。得到了解的存在唯一性结果。

This paper deals with the following problem:u_(it)=u_(ixx), D_r={(x, t): r(t)<x<s(t), O<t<T}, u,(x, O)=φ_i(x),u_(1x)(s(t), t)=-[γ(t)+u_1(s(t), t)](?)(t), u_(1x)(r(t), t)=-[γ(t)+u_1(r(t), t)]r(t),u_2(s(t), t)=[μ(t)-u_2(s(t), t)](?)(t), u_(2x)(r(t), t)=[μ(t)-u_2(r(t), t)](?)(t),(?)(t)=v_1(u_2s(t), t))exp{-δ/u_2(s(t), t)} F_1(u_1(s(t), t)),(?)(t)=v_2(u_2(r(t), t))exp{-δ/u_2(r(t), t)}F_2(u_1(r(t), t)), O<t≤T;The existence and uniqueness of the solution for this problem are obtained. The solution is (u_1, u_2, s, r)