A Note on the Right‐Hand Side Identification Problem Arising in Biofluid Mechanics

Abstract

The inverse problem of reconstructing the right-hand side (RHS) of a mixed problem for one-dimensional diffusion equation with variable space operator is considered. The well-posedness of this problem in Hölder spaces is established.

A note on the numerical solution of an identification problem for observing two‐phase flow in capillaries

“…Proofs of Theorems and follow the same manner given in and are based on the methods given in monograph [, pp. 71‐156].…”

“…Applying difference scheme ([, Eqn (2.61)]), we present the following first order of accuracy difference scheme of the auxiliary problem for the approximate solution of problem …”

“…Over the last two decades, there has been a growing tendency to model some phenomena as inverse problems. In fact, the uncertainty or obscurity on data (conditions and/or coefficient) forces scientists to consider inverse problems [7][8][9][10][11][12][13][14][15][16][17]. In papers [18][19][20][21], flow in capillaries are modeled as direct problem, and in present paper, a specific modeling of a two-phase flow equation with a control parameter p is investigated.…”

“…was investigated in [11]. Here, u.t, x/ and p .t/ are unknown functions; a.x/, b.t, x/, f .t, x/, g.t, x/, .t/, and '.x/ are given sufficiently smooth functions and a.x/ a > 0.…”

Determining of right-hand side of higher order ultraparabolic equation

“…The problems of identifying of one right-hand side function in parabolic, hyperbolic or ultraparabolic equations were considered in [7][8][9][10][11][12][13][14][15][16][17], of the several unknown functions in [6,11,18,19]. The investigation of those problems is based on the method of integral equations and the Shauder principle [11][12][13][14]18], the iterative and regularization methods [17] or the method of successive aproximation [6,7,15,16].…”