Partial Differential Equations in the Complex DomainImproperly posed initial value problems; Integral operators for elliptic equations; Analytic continuation; Pseudoparabilic equations. |
Contents
Contents PHYS | 1 |
IMPROPERLY POSED INITIAL VALUE PROBLEMS | 9 |
INTEGRAL OPERATORS FOR ELLIPTIC EQUATIONS | 36 |
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Common terms and phrases
absolutely and uniformly adjoint equation analytic continuation analytic function arbitrary assume B₂s C₁ Cauchy data Cauchy's coefficients complete family complex variables Consider construct convex Corollary cose defined Ecē elliptic Cauchy problem elliptic equations entire function envelope method equa Exercise exists exponential type f(cose family of solutions figure fundamental solution Goursat problem Helmholtz equation Hence implies improperly posed integral operators inverse Lemma neighbourhood Note origin P₂{f partial differential equation partially analytic plane polynomial Proof Pseudoparabolic Equations radiation pattern regular solution Riemann function Runge approximation property simply connected simply connected domain singularities solution of 9.1 solution of Lu solutions of equation Sommerfeld radiation condition Stefan problem Suppose surface Symmetric Helmholtz Equation Theorem F time-like tion U₂ uniformly and absolutely uniquely determined ΧΩ ди