Partial Differential EquationsNew York University, 1952 - 211 páginas |
Dentro del libro
Resultados 1-3 de 13
Página 3
... givon , this loads to a linear first order P.D.E. for u ( 9 ) having a general solution X ( 10 ) u H ( v ( x , y ) ... Givon two continuously differentiable functions u ( x , y ) and v ( x , y ) , the necessary and sufficient conditions ...
... givon , this loads to a linear first order P.D.E. for u ( 9 ) having a general solution X ( 10 ) u H ( v ( x , y ) ... Givon two continuously differentiable functions u ( x , y ) and v ( x , y ) , the necessary and sufficient conditions ...
Página 65
... givon by tr - 1 ( 42 ) 3 = 1777 5 , w ( r ) ( 0 ) + axx o ( tr - 1 ) and the general m - th crdor derivative by ( 43 ) m t k = 1 , ... , n = from 11 ... 2n w ( r ) ( 0 ) + o ( tr = m ) ཟ dx1 aw .. • a X The functions u and v aro ...
... givon by tr - 1 ( 42 ) 3 = 1777 5 , w ( r ) ( 0 ) + axx o ( tr - 1 ) and the general m - th crdor derivative by ( 43 ) m t k = 1 , ... , n = from 11 ... 2n w ( r ) ( 0 ) + o ( tr = m ) ཟ dx1 aw .. • a X The functions u and v aro ...
Página 118
... givon arbitrarily . du an Wo requiro the condition that du as = 0 . ↓ au We considor one other application of Green's idontity . We take for v a " fundamental " solution . This is a solution that has a singularity at a point which is ...
... givon arbitrarily . du an Wo requiro the condition that du as = 0 . ↓ au We considor one other application of Green's idontity . We take for v a " fundamental " solution . This is a solution that has a singularity at a point which is ...
Contenido
Introduction | 1 |
THE CAUCHY PROBLEM FOR HIGHER ORDER EQUATIONS | 48 |
The Cauchy problem for the general nonlinear | 70 |
Otras 4 secciones no mostradas
Otras ediciones - Ver todas
Términos y frases comunes
analytic function arbitrary boundary data boundary value problem caso Cauchy data Cauchy problem characteristic curves characteristic equation characteristic strips coefficients completes the proof consider considor const continuous function continuous in D+ continuous second converge curvo defined depondent derivativos Dirichlet problem domain dorivatives dxdy easily verified follows formula fundamental solution given givon Green's function Green's identity harmonic function havo heat equation hence honco initial conditions initial curve initial data initial manifold initial value problem integral equation integral surface neighborhood non-characteristic obtain oquation order derivatives order equation ordinary differential equations ordor oxists P₁ power series quantity quasi-linear Riemann function satisfy second order solve suppose tangent theorem tho boundary tho function tho initial Thon thoorom u₁ un+1 uniformly unique valuo vanish variables whore