Partial Differential EquationsNew York University, 1952 - 211 páginas |
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Página 11
Fritz John. y = yo ( s ) the initial values u = u ( s ) are prescribed , X. , Yo , u 。 being continuously ... conditions ( 12 ) u ( x 。( s ) , J 。( s ) ) = u ( s ) Proof : We consider the ordinary differential equations ( 13 ) ax = a ...
Fritz John. y = yo ( s ) the initial values u = u ( s ) are prescribed , X. , Yo , u 。 being continuously ... conditions ( 12 ) u ( x 。( s ) , J 。( s ) ) = u ( s ) Proof : We consider the ordinary differential equations ( 13 ) ax = a ...
Página 28
... initial curve there will exist one and only ono solution z = u ( x , y ) of ( 30 ) containing tho initial strip , i.c. such that z ( x ( s ) , 3 ( 8 ) ) = % ( s ) , 2 ( x ( s ) , y ( s ) ) = P ... initial conditions ( 35 ) X ( s , 0 ) = 28 .
... initial curve there will exist one and only ono solution z = u ( x , y ) of ( 30 ) containing tho initial strip , i.c. such that z ( x ( s ) , 3 ( 8 ) ) = % ( s ) , 2 ( x ( s ) , y ( s ) ) = P ... initial conditions ( 35 ) X ( s , 0 ) = 28 .
Página 80
Fritz John. It is clear that the initial value problem ( 9 ) , ( 11 ) , and ( 12 ) is a special case of this one , so ... conditions will be homogeneous , 1.0 . vanish . This is dono by introducing new depondent functions Af wilere 21 q11 ...
Fritz John. It is clear that the initial value problem ( 9 ) , ( 11 ) , and ( 12 ) is a special case of this one , so ... conditions will be homogeneous , 1.0 . vanish . This is dono by introducing new depondent functions Af wilere 21 q11 ...
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