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A COMPARISON THEOREM FOR SUPER- AND SUBSOLUTIONS OF del(2)u + f(u)=0 AND ITS APPLICATION TO WATER WAVES WITH VORTICITY
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
Russian Acad Sci, Russia.
2019 (English)In: St. Petersburg Mathematical Journal, ISSN 1061-0022, E-ISSN 1547-7371, Vol. 30, no 3, p. 471-483Article in journal (Refereed) Published
Abstract [en]

A comparison theorem is proved for a pair of solutions that satisfy opposite nonlinear differential inequalities in a weak sense. The nonlinearity is of the form f (u) with f belonging to the class L-loc(p) and the solutions are assumed to have nonvanishing gradients in the domain, where the inequalities are considered. The comparison theorem is applied to the problem describing steady, periodic water waves with vorticity in the case of arbitrary free-surface profiles including overhanging ones. Bounds for these profiles as well as streamfunctions and admissible values of the total head are obtained.

Place, publisher, year, edition, pages
AMER MATHEMATICAL SOC , 2019. Vol. 30, no 3, p. 471-483
Keywords [en]
Comparison theorem; nonlinear differential inequality; partial hodograph transform in n dimensions; periodic steady water waves with vorticity; streamfunction
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-157281DOI: 10.1090/spmj/1554ISI: 000464555700007OAI: oai:DiVA.org:liu-157281DiVA, id: diva2:1323796
Note

Funding Agencies|Swedish Research Council (VR) [EO418401]; G. S. Magnusons Foundation of the Royal Swedish Academy of Sciences; Linkoping University

Available from: 2019-06-12 Created: 2019-06-12 Last updated: 2019-06-12

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