Partial Differential EquationsNew York University, 1952 - 211 páginas |
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Página 27
... whore F has continuous second derivatives with respect to its Suppose that along tho initial curve Oss≤ 1 , tho initial valuos z = variables x , y , z , p , q . x = x ( s ) , y = y ( 3 ) , C aro assimod , xo , yo , 20 ( 8 ) Zo having ...
... whore F has continuous second derivatives with respect to its Suppose that along tho initial curve Oss≤ 1 , tho initial valuos z = variables x , y , z , p , q . x = x ( s ) , y = y ( 3 ) , C aro assimod , xo , yo , 20 ( 8 ) Zo having ...
Página 76
... as additional dopendont variablos , 1.0 . considor Pn P11 ••••• Pn as dopondont functions , whore for any Difforentiating with respect to x wo obtain tho u , P1 , ... u , P1 ! = k . oquations n u dxn JP1 11 ( 3 ) = Pin 1 76 .
... as additional dopendont variablos , 1.0 . considor Pn P11 ••••• Pn as dopondont functions , whore for any Difforentiating with respect to x wo obtain tho u , P1 , ... u , P1 ! = k . oquations n u dxn JP1 11 ( 3 ) = Pin 1 76 .
Página 81
... whore we note that In This then leads to cortain rocursion formulae ( 27 ) ( Ê ̧ + 1 ) oÎ ̧ ‚ ............... 1,1 + 1 = P11 , ... , ( a , b , ok , ... , n i = 1 , ... , N which together with the initial conditions C1 = 0 , for xn can be ...
... whore we note that In This then leads to cortain rocursion formulae ( 27 ) ( Ê ̧ + 1 ) oÎ ̧ ‚ ............... 1,1 + 1 = P11 , ... , ( a , b , ok , ... , n i = 1 , ... , N which together with the initial conditions C1 = 0 , for xn can be ...
Contenido
Introduction | 1 |
THE CAUCHY PROBLEM FOR HIGHER ORDER EQUATIONS | 48 |
The Cauchy problem for the general nonlinear | 70 |
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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