Partial Differential Equations, Volumen1New York University [Institute of Mathematical Sciences], 1953 - 422 páginas |
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... equation in two dimensions .. 113 6 . The Dirichlet problem . 124 7 . The Green's function and the fundamental solution .. 142 8 . Equations related to the potential equation .. 9 . Continuation of harmonic functions . 10. The heat equation ...
... equation in two dimensions .. 113 6 . The Dirichlet problem . 124 7 . The Green's function and the fundamental solution .. 142 8 . Equations related to the potential equation .. 9 . Continuation of harmonic functions . 10. The heat equation ...
Página 5
... heat equation " , is satisfied by the temperature distribution of a body conducting heat , provided that the density and specific heat of the material are constant . This is again a second order linear equation for u . CHAPTER I 1 . THE ...
... heat equation " , is satisfied by the temperature distribution of a body conducting heat , provided that the density and specific heat of the material are constant . This is again a second order linear equation for u . CHAPTER I 1 . THE ...
Página 173
... heat equation for t > 0. Moreover K ( x - 5 , t ) = 0 for all x , = 0 for all x , if x is held fixed . However this function as a function of x and t is not continuous , not even bounded , at t = 0 , x = { . In fact the limiting value ...
... heat equation for t > 0. Moreover K ( x - 5 , t ) = 0 for all x , = 0 for all x , if x is held fixed . However this function as a function of x and t is not continuous , not even bounded , at t = 0 , x = { . In fact the limiting value ...
Contenido
CHAFTER I | 6 |
The general first order equation for a function | 15 |
CHAFTER II | 48 |
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Partial Differential Equations: Theory and Completely Solved Problems T. Hillen,I.E. Leonard,H. van Roessel Vista previa limitada - 2019 |
Términos y frases comunes
analytic function arbitrary boundary data boundary value problem Cauchy data Cauchy problem characteristic curves characteristic equations characteristic strips coefficients completes the proof consider const converge defined directional derivative Dirichlet problem domain dxdy easily verified existence follows formula fundamental solution given Green's function Green's identity harmonic function heat equation hence homogeneous equation initial conditions initial curve initial data initial manifold initial surface initial value problem integral equation integral surface Lemma LIBRARIES STANFORD UNIVERSITY neighborhood non-characteristic normal derivative obtain oquation order equation ordinary differential equations parameter family partial differential equation power series quantity quasi-linear Riemann function satisfy solve STANFORD UNIVERSITY LIBRARIES Suppose tangent theorem un+1 uniformly unique UNIVERSITY LIBRARIES STANFORD vanish wave equation whore X₁ әх