The rating curve is the relationship between the water stage and the associated discharge in a givensection of a channel. In steady flow, this relationship usually has exponential type, whereas inunsteady it flow has a looped shape. Since direct developing of actual looped rating curve by usinghydrometric methods is merely possible, steady-state rating curve is commonly used as a downstreamboun...

We prove that if the given compact set K is convex then a minimizer of the functional I(v) = ∫ BR |∇v|dx + Per({v > 0}), 1 < p < ∞, over the set {v ∈ H 0 (BR)| v ≡ 1 on K ⊂ BR} has a convex support, and as a result all its level sets are convex as well. We derive the free boundary condition for the minimizers and prove that the free boundary is analytic and the minimizer is unique.

We show that a minimal disk satisfying the free boundary condition in a constant curvature ball of any dimension is totally geodesic. We weaken the condition to parallel mean curvature vector in which case we show that the disk lies in a three dimensional constant curvature submanifold and is totally umbilic. These results extend to higher dimensions earlier three dimensional work of J. C. C. N...

Sensitive boundary condition dependence (BCD) is reported in a convectively unstable system with noise, where the amplitude of generated oscillatory dynamics in the downstream depends sensitively on the boundary value. This BCD is explained in terms of the decrease (relaxation) of the comoving Lyapunov exponent (characterizing the convective instability) from upstream to downstream [K. Fujimoto...

The development of phase change models applicable to a wide range temperatures, pressures, and mass flow rates is primarily limited by the metastable or partially stable behaviour fluid. Due this, fluid does not even after crossing saturation conditions. Most liquid–vapour have been developed for cavitation process where sustained, occurs in very narrow region space, under equilibrium In this p...

Abstract. The problem of Rayleigh–Bénard convection with internal heat sources and a variable gravity field is treated. For the case of stress-free boundary conditions, it is proved that the principle of exchange of stabilities holds as long as the product of gravity field and the integral of the heat sources is nonnegative throughout the layer. The proof is based on the idea of a positive oper...

The paper is concerned with linear thermoelastic plate equations in a domain Ω: utt +∆u+∆θ = 0 and θt −∆θ −∆ut = 0 in Ω× (0,∞), subject to Dirichlet boundary condition: u|Γ = Dνu|Γ = θ|Γ = 0 and initial condition: (u, ut, θ)|t=0 = (u0, v0, θ0) ∈W 2 p,D(Ω)×Lp×Lp. Here, Ω is a bounded or exterior domain in R (n ≥ 2). We assume that the boundary Γ of Ω is a C hypersurface and we define W 2 p,D by ...

We show herein the uniform stability of a thermoelastic plate model with no added dissipative mechanism on the boundary (uniform stability of a thermoelastic plate with added boundary dissipation was shown in [J. LAGNESE, Boundary Stabilization of Twin Plates, SIAM Stud. Appl. Math. 10, SIAM, Philadelphia, PA, 1989], as was that of the analytic case—where rotational forces are neglected—in [Z. ...

We study a 2-phase free boundary problem for harmonic measure first considered by Kenig and Toro [KT06] and prove a sharp Hölder regularity result. The central difficulty is that there is no a priori non-degeneracy in the free boundary condition. Thus we must establish non-degeneracy by means of monotonicity formulae.