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Parabolic Equations in One Space Variable
Parabolic Equations in Two Space Variables
2 other sections not shown
analytic function analytic solutions approach approximate approximate solution arbitrarily assume assumption boundary boundary value problems bounded classical solution coefficients complete family conclude consider construct contained converges CRUZ defined denotes determined differential equation Dirichlet discussion domain elliptic equations entire function exists exterior fact family of solutions flow formula given gives heat equation hence Hölder continuous implies independent independent variables initial-boundary value problem integral equation integral operator inverse Stefan problem known look loss manner maps method neighbourhood Note numerical obtain origin parabolic equations particular plane polynomial positive constant potential Proof real valued solution recursion represented respect satisfies seen singularity solution of L[u solve space variables Substituting t)ds Theorem theory twice continuously differentiable uniformly uniquely University Library Volterra xy(t zero