Partial Differential EquationsNew York University, 1952 - 211 páginas |
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Página 15
... ordor partial differential oquation for a function of two variables z ( x , y ) and its derivatives = q can be written = zx P , z Z3 J ( 1 ) F ( x , y , z , p , q ) = 0 . It will bo assumod that has continuous second derivatives with ...
... ordor partial differential oquation for a function of two variables z ( x , y ) and its derivatives = q can be written = zx P , z Z3 J ( 1 ) F ( x , y , z , p , q ) = 0 . It will bo assumod that has continuous second derivatives with ...
Página 61
... ordor dorivativo on S ( 30 ) 1 ax1 mu axn in ( m ) n from which will follow oquation ( 29 ) . This is dono by induction . For m = 1 oquation ( 30 ) is just equation ( 23 ) . Assume equation ( 30 ) truo for all km - 1 . Note that this ...
... ordor dorivativo on S ( 30 ) 1 ax1 mu axn in ( m ) n from which will follow oquation ( 29 ) . This is dono by induction . For m = 1 oquation ( 30 ) is just equation ( 23 ) . Assume equation ( 30 ) truo for all km - 1 . Note that this ...
Página 76
... ordor can bo reduced to a non - characteristic initial value problem for a quasi - linear system of P.D.E. of first ordor . Proof . We will prove this theorom for the second order P.D.E. ( 1 ) and initial data ( 6 ) which we are ...
... ordor can bo reduced to a non - characteristic initial value problem for a quasi - linear system of P.D.E. of first ordor . Proof . We will prove this theorom for the second order P.D.E. ( 1 ) and initial data ( 6 ) which we are ...
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