On noncompact Hammerstein integral equations and a nonlinear boundary value problem for the heat equation. (English) Zbl 0766.45003
The author studies the solvability of noncompact Hammerstein integral equations of Volterra and Wiener-Hopf types. He obtains the \(L^ \infty\)-theory from the known \(L^ 2\)-theory by using a result related to Hadamard’s theorem. Finally he solves a boundary value problem for the heat equation in a half plane with nonlinear radiation on the boundary.
Reviewer: J.Schönenberger-Deuel (Männedorf)
MSC:
| 45G10 | Other nonlinear integral equations |
| 45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
| 35K05 | Heat equation |
| 35K60 | Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations |
Keywords:
nonlinear boundary value problem; Volterra equation; Wiener-Hopf equation; noncompact Hammerstein integral; heat equationReferences:
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