On a forward-backward parabolic equation
In: Annali di Matematica Pura ed Applicata, Jg. 90 (1971-12-01), S. 1-57
Online
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Zugriff:
Boundary value problems for the equation $$\operatorname{sgn} (x) \cdot u_y - u_{xx} + ku = f(x,y)$$ (where k is a positive constant and † is a given function) are investigated. The domain of the solutions will be the whole upper half-plane y>0, or the half-plane y>0 cut along the positive y-axis. We are interested in square integrable solutions u, with square integrable generalized derivatives uy and uxx. Existence theorems are proved, with an integral equations technique. Thus a theory is developed of Wiener-Hopf integral equations of the first kind with solutions belonging to Sobolev spaces.
Titel: |
On a forward-backward parabolic equation
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Autor/in / Beteiligte Person: | Talenti, G. ; Pagani, C. D. |
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Zeitschrift: | Annali di Matematica Pura ed Applicata, Jg. 90 (1971-12-01), S. 1-57 |
Veröffentlichung: | Springer Science and Business Media LLC, 1971 |
Medientyp: | unknown |
ISSN: | 1618-1891 (print) ; 0373-3114 (print) |
DOI: | 10.1007/bf02415041 |
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