A Free Boundary Problem for a Diffusion-Convection Equation with Nonlocal Condition

Authors

  • Takhirov J. V. I. Romanovskiy Institute of Mathematics, Academy of Sciences of Uzbekistan, Tashkent, Uzbekistan Author
  • Rasulov M. V. I. Romanovskiy Institute of Mathematics, Academy of Sciences of Uzbekistan, Tashkent, Uzbekistan, Tashkent State Transport University, Tashkent, Uzbekistan Author

DOI:

https://doi.org/10.29229/uzmj.2026-3-19

Keywords:

free boundary, diffusion-convection, parabolic equation, a priori bounds, existence and uniqueness

Abstract

In this paper, we consider a free boundary problem for a diffusion-convection equation with a nonlocal boundary condition. Methods for obtaining a priori estimates in the norms of Hölder spaces for the solution are proposed. On the basis of these estimates, the existence and uniqueness of the solution are proved.

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Published

2026-10-06

Issue

Vol. 70 No. 3 (2026)

Section

Published

How to Cite

A Free Boundary Problem for a Diffusion-Convection Equation with Nonlocal Condition. (2026). Uzbek Mathematical Journal, 70(3), 181-189. https://doi.org/10.29229/uzmj.2026-3-19