Partial Differential EquationsNew York University, 1952 - 211 páginas |
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Página 20
... given partial differential equation . Supposo we are given an integral surface z = z ( x , y ) having continuous second derivatives with respect to x and y . At each point the surface will bo tangent to a Monge cono . See figure below ...
... given partial differential equation . Supposo we are given an integral surface z = z ( x , y ) having continuous second derivatives with respect to x and y . At each point the surface will bo tangent to a Monge cono . See figure below ...
Página 34
... given initial curve will be a solution containing this curve . This envelope may consist of several shocts corresponding to the various integral surfaces which may pass through the given curvo . A complete integral z = f ( x , y , a , b ) ...
... given initial curve will be a solution containing this curve . This envelope may consist of several shocts corresponding to the various integral surfaces which may pass through the given curvo . A complete integral z = f ( x , y , a , b ) ...
Página 42
... given an integral of the form ( 16 ) D = ex ( xx ) i dx , dxxx xn at at at 81k = for a given curvo x ( t ) , i = 1 , ... , n . Assuming that the quantity under the radical is non - nogativo , tho integral can be interpreted as dcfining ...
... given an integral of the form ( 16 ) D = ex ( xx ) i dx , dxxx xn at at at 81k = for a given curvo x ( t ) , i = 1 , ... , n . Assuming that the quantity under the radical is non - nogativo , tho integral can be interpreted as dcfining ...
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