This monograph presents new theory and methods of solving inverse
Stefan problems for quasilinear parabolic equations in domains with
free boundaries. This new approach to the theory of ill-posed
problems is useful for the modelling of nonlinear processes with
phase transforms in thermophysics and mechanics of continuous
media. Regularization methods and algorithms are developed for the
numerical solution of inverse Stefan problems ensuring substantial
savings in computational costs. Results of calculations for
important applications in a continuous casting and for the
treatment of materials using laser technology are also given. This
text should be of interest to students and researchers whose work
involves partial differential equations, numerical analysis, phase
transformation, mathematical modelling, industrial mathematics and
the mathematics of physics.
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