Techniques in Partial Differential Equations |
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Page 131
... elliptic PDE into the canonical form Uaα + UBB + lower - order terms = 0 As emphasized previously , the type of equation may vary from point to point . If the coefficients of the PDE are continuous , however , an equation which is elliptic ...
... elliptic PDE into the canonical form Uaα + UBB + lower - order terms = 0 As emphasized previously , the type of equation may vary from point to point . If the coefficients of the PDE are continuous , however , an equation which is elliptic ...
Page 142
... elliptic equation one boundary condition on the boundary of a bounded domain is all that can be given . For higher - order elliptic equations ( we can assume the order is even or else the equation could not be elliptic in the first ...
... elliptic equation one boundary condition on the boundary of a bounded domain is all that can be given . For higher - order elliptic equations ( we can assume the order is even or else the equation could not be elliptic in the first ...
Page 239
Clive R. Chester. 10 Linear Elliptic Equations 10-1 . INTRODUCTION As pointed out in Chap . 6 , the most general linear elliptic second - order partial differential equation ( PDE ) in n independent variables is n n Zajk ( X ) Uxjxx + ...
Clive R. Chester. 10 Linear Elliptic Equations 10-1 . INTRODUCTION As pointed out in Chap . 6 , the most general linear elliptic second - order partial differential equation ( PDE ) in n independent variables is n n Zajk ( X ) Uxjxx + ...
Common terms and phrases
analytic arbitrary function assume axis called canonical form Cauchy problem Chap characteristic curves characteristic directions characteristic equations coefficients complete integral cone constant coordinates defined DEFINITION depend derivatives determine dimensions Dirichlet problem domain dual integral equations elliptic end point Euler's equation family of characteristics first-order PDE function u(x given Green's function Green's identity Hamilton-Jacobi equation Hamilton's equations harmonic function Hence homogeneous hyperbolic equation independent variables infinity initial curve integral equation integral surface Laplace transform Math method Neumann problem nonhomogeneous nonlinear obtain ODEs one-parameter family P₁ parameter Partial Differential Equations piston Poisson's potential equation prescribed quasi-linear region satisfy second-order linear solution solve space spacelike Suppose Theorem timelike V²u vanishes vector velocity wave equation xy plane zero