We investigate regularity and well-posedness for a fluid evolution model in the presence of a three-phase contact point. We consider a fluid evolution governed by Darcy’s Law. After linearization, we obtain a nonlocal third order operator which contains the Dirichlet-Neumann operator on the wedge with opening angle > 0. We show well-posedness and regularity for this linear evolution equation. I...

This paper completes a previous work on a Black and Scholes equation with stochastic volatility. This is a degenerate parabolic equation, which gives the price of a European option as a function of the time, of the price of the underlying asset, and of the volatility, when the volatility is a function of a mean reverting Orstein–Uhlenbeck process, possibly correlated with the underlying asset. ...

A Lie algebra g is Frobenius if it admits a linear functional F ∈ g * such that the Kirillov form BF (x, y) = F ([x, y]) is non-degenerate. If g is the mth maximal parabolic subalgebra P(n, m) of sl(n) this occurs precisely when (n, m) = 1. We define a cyclic functional F on P(n, m) and prove it is non-degenerate using properties of graphs associated to F. These graphs also provide in certain c...

We investigate the effect of small diffusion on principal eigenvalues linear time-periodic parabolic operators with zero Neumann boundary conditions in one dimensional space. The asymptotic behaviors eigenvalues, as coefficients tend to zero, are established for non-degenerate and degenerate spatial-temporally varying environments. A new finding is dependence these periodic solutions a specific...

This paper presents a new mathematical technique for the identification of two rheological model functions (namely, the hindered settling and effective solid stress functions) obtained from concentration profiles measured during the centrifugation of flocculated suspensions. We consider both a rotating tube and a basket centrifuge at a given angular velocity, and assume that the radius (i.e., t...

We study the influence of thermal fluctuations on the dewetting dynamics of thin liquid films. Starting from the incompressible Navier-Stokes equations with thermal noise, we derive a fourth-order degenerate parabolic stochastic partial differential equation which includes a conservative, multiplicative noise term—the stochastic thin-film equation. Technically, we rely on a long-wave-approximat...

The model is a subdiffusion-type fractional degenerate parabolic equation. We consider two inverse source problems with power vertical diffusion coefficients, including the well-known Monin-Obukhov atmospheric model. Final-time over-determination condition posed. Solutions to both are expressed in series expansion. Numerical examples discussed.

Models of self-organizing bacterial communities and comparisons with experimental observations. dynamics with size dependency–strain phenomena. [4] Benoˆıt Perthame. Why hyperbolic and kinetic models for cell populations self-organization? In Hyperbolic problems: theory, numerics and applications , volume 67 of Proc. The non-local Fisher-KPP equation: travelling waves and steady states. [8] Phi...

This article is devoted to the study of null controllability properties for two systems of coupled one dimensional degenerate parabolic equations. The first system consists of two forward equations, while the second one consists of one forward equation and one backward equation. Both systems are in cascade, that is, the solution of the first equation acts as a control for the second equation an...

Večeř derived a degenerate parabolic equation with a boundary condition characterizing the price of Asian options for both discrete and continuous arithmetic average. It is well understood that there exists a unique probabilistic solution to such a problem. However, due to degeneracy of the partial differential operator and lack of smoothness in the boundary data, the regularity of the probabil...