STEEP WELL

Existence and concentration of solutions for the nonlinear Kirchhoff type equations with steep well potential

The existence of nontrivial solution for a class of sublinear biharmonic equations with steep potential well

where 2u = ( u), N > 4, λ > 0, 1 < q < 2 and μ ∈ [0,μ0], 0 < μ0 <∞. The continuous function f verifies the assumptions: (f1) f (s) = o(|s|) as s→ 0; (f2) f (s) = o(|s|) as |s| →∞; (f3) F(u0) > 0 for some u0 > 0, where F(u) = ∫ u 0 f (t) dt. According to hypotheses (f1)–(f3), the number cf = max s =0 | f (s) s | > 0 is well defined (see [1]). The continuous functions α and K verify the assumptio...

Quasiplanar steep water waves.

A unique description for highly nonlinear potential water waves is suggested, where weak three-dimensional effects are included as small corrections to exact two-dimensional equations written in conformal variables. Contrary to the traditional approach, a small parameter in this theory is not a surface slope, but it is the ratio of a typical wavelength to a large transversal scale along the sec...

Antidunes on steep slopes

16 When increasing the rates of subcritical flow on gentle slopes, the bed successively produces 17 ripples, dunes and flat beds. Antidunes (defined here as all bed undulations for which the 18 surface gravity waves are in phase with the bed profile) appear only in high flow rates and 19 may be found in some extreme natural flow events. Inversely, on steep slopes flume 20 experiment (S≥1% appro...

Kinematics of steep bedrock permafrost

[1] The mechanisms that control climate-dependent rockfall from permafrost mountain slopes are currently poorly understood. In this study, we present the results of an extensive rock slope monitoring campaign at the Matterhorn (Switzerland) with a wireless sensor network. A negative dependency of cleft expansion relative to temperature was observed at all clefts for the dominant part of the yea...