摘要
研究了高阶波动方程具有奇性斜导数的混和问题(Ⅰ)场v在Г的子流形Г_0上与Г相切,而与Г_0横截,dimГ_0=dimГ-1≥1,且边界向量场通过此流形的邻域不变号(或由正到负)时,证明了若f∈H^(s-3,s-3)(Q),g_1∈H^(s-1/2,s-1/2)(?Q),g_2∈H^(s-5/2,s-5/2)(?Q),u_j∈H^(s+1)(Ω),且满足相容条件(补充条件),则问题(Ⅰ)有唯一解u∈H^(s,s)(Q).
In this paper we consider the problemOur main result is as follows: Assume that v is tangent to Γ on its submanifold Γ0,v is transversal to Γ0. and dim Γ0=dimΓ-1≥1, and the boundary vector field does not change sign (or sign from positive to negative), as it passes a neighborhood of Γ0, and f ∈ Hg-3,g-3(Q),g1 ∈ satisfying the compatibity condition (adding the complement condition), then the problem (I) has a unique solution a ∈H5,5(Q).
出处
《四川大学学报（自然科学版）》
CAS
CSCD
1992年第4期451-456,共6页
Journal of Sichuan University(Natural Science Edition)
关键词
波动方程
奇性斜导数
向量场
singular oblique derivative, vector field, mixed problem, wave equation.
