5 papers
Nonlocal degenerate parabolic hyperbolic equations on bounded domains. Part II: Existence
Jørgen Endal, Espen R Jakobsen, Ola Mæhlen
We study well-posedness of degenerate mixed-type parabolic-hyperbolic equations on bounded domains with general Diric…
Transport equations for Osgood velocity fields
Ulrik Skre Fjordholm, Ola Isaac Høgåsen Mæhlen
We consider the transport equation with a velocity field satisfying the Osgood condition. The weak formulation is not meaningful in the usual Lebesgue sense, meaning that the usual…
Asymmetric travelling wave solutions of the capillary-gravity Whitham Equation
Ola Mæhlen, Douglas Svensson Seth
By a bifurcation argument we prove that the capillary-gravity Whitham equation features asymmetrical periodic travelling wave solution of arbitrarily small amplitude. Such waves ex…
Solitary waves for weakly dispersive equations with inhomogeneous nonlinearities
Ola Maehlen
We show existence of solitary-wave solutions to the equation \begin{equation*} u_t+ (Lu - n(u))_x = 0\,, \end{equation*} for weak assumptions on the dispersion and the nonlinea…
On the bifurcation diagram of the capillary-gravity Whitham equation
Mats Ehrnström, Mathew A. Johnson, Ola I. H. Maehlen +1
We study the bifurcation of periodic travelling waves of the capillary-gravity Whitham equation. This is a nonlinear pseudo-differential equation that combines the canonical shallo…