Geodesic
On the Global-in-Time Existence of a Generalized Solution to a Free-Boundary Problem
Matematičeskie zametki, Tome 107 (2020) no. 2, pp. 229-240

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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.
Keywords: free-boundary problems, fixed-point method, a priori estimates.
Mots-clés : diffusion-convection equation 
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     author = {A. M. Meirmanov and O. A. Galtseva and V. E. Seldemirov},
     title = {On the {Global-in-Time} {Existence} of a {Generalized} {Solution} to a {Free-Boundary} {Problem}},
     journal = {Matemati\v{c}eskie zametki},
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     year = {2020},
     language = {ru},
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A. M. Meirmanov; O. A. Galtseva; V. E. Seldemirov. On the Global-in-Time Existence of a Generalized Solution to a Free-Boundary Problem. Matematičeskie zametki, Tome 107 (2020) no. 2, pp. 229-240. http://geodesic.mathdoc.fr/item/MZM_2020_107_2_a5/