For a linear transport equation in one space dimension with speeds in a compact interval and a general symmetric kernel for the change of velocity a problem with free boundary (Stefan problem) is stated. The case of constant speed corresponds to a Stefan problem for the damped wave equation (telegraphers equation). Existence and uniqueness of the free boundary is shown, and the connection to th...

A model for species diffusion is presented, with evaporation at a moving free boundary. The resulting problem resembles a one-phase Stefan problem with superheating, but the usual Stefan condition at the moving boundary is replaced by a version which, in the classical setting, would violate conservation of energy. In the fast evaporation limit, however, the problem reduces to a classical nonlin...

The Chen groups of a finitely-presented group G are the lower central series quotients of its maximal metabelian quotient, G/G′′. The direct sum of the Chen groups is a graded Lie algebra, with bracket induced by the group commutator. If G is the fundamental group of a formal space, we give an analog of a basic result of D. Sullivan, by showing that the rational Chen Lie algebra of G is isomorp...

My research interests span the areas of systems, programming languages, and security. I particularly enjoy building secure systems that can see adoption. My efforts are generally guided by two goals: (1) to enable average developers to build secure systems and applications, and (2) to leverage the benefits of formal semantics when reasoning about the security properties of a system. For example...

The ability to restore a virtual platform from a previously saved simulation state can considerably shorten the typical edit-compile-debug cycle for software developers and therefore enhance productivity. For SystemC based virtual platforms (VP), dedicated checkpoint/restore (C/R) solutions are required, taking into account the specific characteristics of such platforms. Apart from restoring th...

in this paper, we present a fractional mathematical model of a one-dimensional phase phase change problem (stefan problem) with latent heat a power function of position. this model includes space-time fractional derivatives in caputo sense and time dependent surface heat flux. an approximate solution of this model is obtained by optimal homotopy asymptotic method (oham) to find an approximate s...

We develop a high-order energy method to prove asymptotic stability of flat steady surfaces for the Stefan problem with surface tension also known as the Stefan problem with Gibbs-Thomson correction.

The supercooled Stefan problem and its variants describe the freezing of a liquid in physics, as well large system limits systemic risk models finance integrate-and-fire neuroscience. Adopting physics terminology, is known to feature finite-time blow-up rate for wide range initial temperature distributions liquid. Such can result discontinuity liquid-solid boundary. In this paper, we prove that...

One and two phase Stefan problems for the linear heat equation have been the subject of many studies in the past [1, 2]. Indeed these problems have a great physical relevance since they provide a mathematical model for the processes of phase changes [3, 4]. The boundary between the two phases is a free boundary: its motion has to be determined as part of the solution. More recently the previous...