In this review, concerning parabolic equations, we give self-contained descriptions on (1)
derivations of Carleman estimates;(2) methods for applications of the Carleman estimates to …

The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

This book presents an account of theories of? ow in porous media which have proved
tractable to analysis and computation. In particular, the t-ories of Darcy, Brinkman, and …

As we navigate through life we instinctively model time as having a flowing present that
divides a fixed past from open future. This model develops in childhood and is deeply …

We consider a backward problem in time for a time-fractional partial differential equation in
one-dimensional case, which describes the diffusion process in porous media related with …

The recent modification of the Cattaneo equations proposed by Christov is analysed. The
solution to both the initial and final value problems is shown to be unique. Further, it is …

It is known that in the case that several constitutive tensors fail to be positive definite the
system of the thermoelasticity could become unstable and, in certain cases, ill-posed in the …

The subject of blow-up in a finite time, or at least very rapid growth, of a solution to a partial
differential equation has been an area of intense re search activity in mathematics. Some …

The Brinkman–Forchheimer equations for non‐slow flow in a saturated porous medium are
analyzed. It is shown that the solution depends continuously on changes in the Forchheimer …

In this paper we approach the linear mixed problem with initial and boundary values for a
Cosserat body which is elastic and has pores. We coupled the equations characterizing the …