arXiv subjects

Pham Hoang Quan

Publications and source records attributed to Pham Hoang Quan.

4 recordsLinked to original sources

arXiv2011

Ice formation in the Arctic during summer: false-bottoms

The only source of ice formation in the Arctic during summer is a layer of ice called false-bottoms between an under-ice melt pond and the underlying ocean. Of interest is to give a mathematical model in order to determine the simultaneous growth and ablation of false-bottoms, which is governed by both of heat fluxes and salt fluxes. In one dimension, this problem may be considered mathematically as a two-phase Stefan problem with two free boundaries. Our main result is to prove the existence and uniqueness of the solution from the initial condition.

math.AP↗

arXiv2009

A new stability results for the backward heat equation

In this paper, we regularize the nonlinear inverse time heat problem in the unbounded region by Fourier method. Some new convergence rates are obtained. Meanwhile, some quite sharp error estimates between the approximate solution and exact solution are provided. Especially, the optimal convergence of the approximate solution at t = 0 is also proved. This work extends to many earlier results in (f2,f3, hao1,Quan,tau1, tau2, Trong3,x1).

math.AP↗

arXiv2007

A nonlinearly ill-posed problem of reconstructing the temperature from interior data

We consider the problem of reconstructing, from the interior data $u(x,1)$, a function $u$ satisfying a nonlinear elliptic equation $$ Δu = f(x,y,u(x,y)), x \in \RR, y > 0. $$

math.AP↗

arXiv2007

Sinc Approximation of the Heat Distribution on the Boundary of a Two-Dimensional Finite Slab

We consider the two-dimensional problem of recovering globally in time the heat distribution on the surface of a layer inside of a heat conducting body from two interior temperature measurements. The problem is ill-posed. The approximation function is represented by a two-dimensional Sinc series and the error estimate is given.

math.AP↗