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Search: L773:1873 1449 > (2015-2019) > (2019)

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1.
  • Ehrnström, Mats, et al. (author)
  • On Whitham's conjecture of a highest cusped wave for a nonlocal dispersive equation
  • 2019
  • In: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire. - : European Mathematical Society - EMS - Publishing House GmbH. - 0294-1449 .- 1873-1430. ; 36:6, s. 1603-1637
  • Journal article (peer-reviewed)abstract
    • We consider the Whitham equation u t +2uu x +Lu x =0, where L is the nonlocal Fourier multiplier operator given by the symbol m(ξ)=tanh⁡ξ/ξ. G. B. Whitham conjectured that for this equation there would be a highest, cusped, travelling-wave solution. We find this wave as a limiting case at the end of the main bifurcation curve of P-periodic solutions, and give several qualitative properties of it, including its optimal C 1/2 -regularity. An essential part of the proof consists in an analysis of the integral kernel corresponding to the symbol m(ξ), and a following study of the highest wave. In particular, we show that the integral kernel corresponding to the symbol m(ξ) is completely monotone, and provide an explicit representation formula for it. Our methods may be generalised.
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2.
  • Strömqvist, Martin, 1982- (author)
  • Harnack's Inequality for Parabolic Nonlocal Equations
  • 2019
  • In: Annales de l'Institut Henri Poincare. Analyse non linéar. - : European Mathematical Society - EMS - Publishing House GmbH. - 0294-1449 .- 1873-1430. ; 36:6, s. 1709-1745
  • Journal article (peer-reviewed)abstract
    • The main result of this paper is a nonlocal version of Harnack's inequality for a class of parabolic nonlocal equations. We additionally establish a weak Harnack inequality as well as local boundedness of solutions. None of the results require the solution to be globally positive.
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  • Result 1-2 of 2
Type of publication
journal article (2)
Type of content
peer-reviewed (2)
Author/Editor
Strömqvist, Martin, ... (1)
Wahlén, Erik (1)
Ehrnström, Mats (1)
University
Uppsala University (1)
Lund University (1)
Language
English (2)
Research subject (UKÄ/SCB)
Natural sciences (2)
Year
2019 (2)Undo refine

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