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On the global in-time existence of generalized solution to a free boundary problem

Mathematical notes. 2020. Vol. 107. P. 274–283.
Meirmanov A. M., Gal’tseva O. A., Sel’demirov V. E.

A problem with free (unknown) boundary for a one-dimensional diffusion-convection equation is considered. The unknown boundary is found from an additional condition on the free boundary. By the extension of the variables, the problem in an unknown domain is reduced to an initial boundary-value problem for a strictly parabolic equation with unknown coefficients in a known domain. These coefficients are found from an additional boundary condition that enables the construction of a nonlinear operator whose fixed points determine a solution of the original problem.

Priority areas: mathematics
Language: English
DOI
Text on another site
Keywords: a priori estimatesfree-boundary problemsdiffusion-convection equationfixed-point method
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