弾性論の初期境界値問題における解の連続依存性について

概要

論文の詳細を見る
Let G be a bounded domain in R^p, G^^- its closure, and we assume that the boundary ∂G of G^^- is piceewise smooth. Let u be a displacement vector with components u_j, τ(u) a stress tensor with components τ_<jk>(u), n the unit outward normal on ∂G, 0<p<+∞ a density of elastic media, 0<λ<+∞ and 0<μ<+∞ Lame's coefficients, and F denotes a body force with component F_j. We assume λ, μ∈C^1(G)∩C(G^^-), ρ∈C(G^^-), F_j∈C(Ω^^-_T), where Ω_T=G×(0,T), 0<T<+∞. Consider the equation [numerical formula] defined in Ω_T together with the initial conditions [numerical formula] and one of the following boundary conditions on ∂G: a) [numerical formula] b) [numerical formula] Here α is a constant that α=0 or α=1, x is a space variable in G^^-, t is a time variable in [0,T]. When we adopt the boundary condition (***)-a), we denote u_0, u_1∈C^2(G)∩C^1(G^^-). Similarly, for the case (***)-b), we denote u_0, u_1∈C^2(G)∩C^1(G∪∂_1G∪(∂G-<∂_1G>^^^-. A solution of problem (*), (**), (***)-a) is called regular if it belongs to C^2(Ω_T)∩C^1(Ω_T). We call a solution of problem (*), (**), (***)-b) is regular if it belongs to C^2(Ω_T)∩C^1((G∪∂_1G∪(∂G-<∂_1G>^^^-))×[0,T]). In this note we show the following results: Proposition We denote by u^^〜 a solution of (*)-(***) under the condition F^^〜, u^^〜_0, u^^〜_1 with the same smoothness for that of F, u_0, u_1, respectively. For ε, ε_0, ε_1>0, if we have [numerical formula], then any regular solution u, u^^〜 of the problem (*)-(***) satisfy the inequalities [numerical formula], [numerical formula], [numerical formula], [numerical formula], where A is a certain constant, e_<jk> is strain component, ||・|| is usual L^2 seminorm, and [numerical formula] Corollary The regular solution of problem (*)-(***) is unique.
明治大学の論文

著者

古橋朗蔵
明治大学大学院

弾性論の初期境界値問題における解の連続依存性について

スポンサーリンク

概要

著者

関連論文

スポンサーリンク