Variable Transforms 标准形式 22+202n92u a2 drdy ay2 +do+ea+fu +g=0 a,b,c,d,e,f和g是x,y的已知函数 通常假设它们连续可微
Linear PDE (2 order) Classification of PDE’s (2 order) Canonical Forms PDE under Variable Transforms IO/ª a ∂ 2u ∂x2 + 2b ∂ 2u ∂x∂y + c ∂ 2u ∂y2 +d ∂u ∂x + e ∂u ∂y + fu + g = 0 a, b, c, d, e, fÚg´x, y®¼ê Ï~b§ëY ¼êa, b, c¥§kØð0§ÄKÒ Ø¤Ù ©§ C. S. Wu 1Êù C©{ÐÚ
Variable Transforms 标准形式 22+202n92u a2 drdy ay2 +do+ea+fu +g=0 a,b,c,d,e,f和g是x,y的已知函数 ρ通常假设它们连续可微 函数b.C中,至少有一个不恒为0,否则就(类 不成其为二阶偏微分方程
Linear PDE (2 order) Classification of PDE’s (2 order) Canonical Forms PDE under Variable Transforms IO/ª a ∂ 2u ∂x2 + 2b ∂ 2u ∂x∂y + c ∂ 2u ∂y2 +d ∂u ∂x + e ∂u ∂y + fu + g = 0 a, b, c, d, e, fÚg´x, y®¼ê Ï~b§ëY ¼êa, b, c¥§kØð0§ÄKÒ Ø¤Ù ©§ C. S. Wu 1Êù C©{ÐÚ
Variable Transforms 标准形式 22+202n92u a2 drdy ay2 +do+ea+fu +g=0 a,b,c,d,e,f和g是x,y的已知函数 ρ通常假设它们连续可微 函数,bc中,至少有一个不恒为0,否则就( 不成其为二阶偏微分方程
Linear PDE (2 order) Classification of PDE’s (2 order) Canonical Forms PDE under Variable Transforms IO/ª a ∂ 2u ∂x2 + 2b ∂ 2u ∂x∂y + c ∂ 2u ∂y2 +d ∂u ∂x + e ∂u ∂y + fu + g = 0 a, b, c, d, e, fÚg´x, y®¼ê Ï~b§ëY ¼êa, b, c¥§kØð0§ÄKÒ Ø¤Ù ©§ C. S. Wu 1Êù C©{ÐÚ
E under Variable Transforms 讲授要点 二阶线性偏微分方程 自变量变换下的偏微分方程 二阶线性偏微分方程的分类 个定理 双曲型方程 椭圆型方程 抛物型方程
Linear PDE (2 order) Classification of PDE’s (2 order) Canonical Forms PDE under Variable Transforms ùÇ: 1 5 ©§ IO/ª gCþCe ©§ 2 5 ©§©a ½n V.§ ý .§ Ô.§ C. S. Wu 1Êù C©{ÐÚ
E under Variable Transforms 只考虑a和(或)C不恒为0的情形
Linear PDE (2 order) Classification of PDE’s (2 order) Canonical Forms PDE under Variable Transforms ÄaÚ(½)cØð0/ Øa 6≡ 0 C ξ = φ(x, y), η = ψ(x, y) yξÚηE´ÕáCþ§ù|C7L÷v ∂(ξ, η) ∂(x, y) 6= 0 ea = c = 0§K®áue¡Ñ/ C. S. Wu 1Êù C©{ÐÚ