The theory of ill-posed problems originated in an unusual way. As a rule, a new concept is a
subject in which its creator takes a keen interest. The concept of ill-posed problems was …

Driven by the advancement of industrial mathematics and the need for impact case studies,
Inverse Problems with Applications in Science and Engineering thoroughly examines the …

Written by two international experts in the field, this book is the first unified survey of the
advances made in the last 15 years on key non-standard and improperly posed problems for …

A mollification method for a class of ill-posed problems is suggested. The idea of the method
is very simple and natural: if the data are given inexactly then we try to find a sequence …

We consider a Cauchy problem for the heat equation in the quarter plane, where data are
given at x= 1 and a solution is sought in the interval 0< x< 1. This sideways heat equation is …

In this article, we investigate an inverse and ill-posed problem to simultaneously reconstruct
the space-dependent source and initial value associated with a two-dimensional heat …

We consider a Cauchy problem for the heat equation in the quarter plane, where data are
given at x= 1 and a solution is sought in the interval 0< x< 1. This sideways heat equation is …

In this paper, we consider a two-dimensional time-fractional inverse heat conduction
problem, which is severely ill-posed. A quasi-reversibility method is proposed to solve this …

In this paper we consider the following ill-posed Cauchy problem for the heat equation in the
half-plane: given noisy data us (L, i) to u (x, i) along the line χ= L, determine the solution u (x …

The inverse heat conduction problem (IHCP) can be considered to be a sideways parabolic
equation in the quarter plane, and now the results available in the literature on IHCP mainly …