Solution of the nonregular problem for a parabolic equation with the time derivative in the boundary condition

Article type: Research Article

Authors: Bizhanova, Galina^{; *}

Affiliations: Institute of Mathematics and Mathematical Modeling, Pushkin str., 125, Almaty 050010, Kazakhstan. E-mail: [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: There is studied the Hölder space solution uε of the problem for parabolic equation with the time derivative ε∂tuε|Σ in the boundary condition, where ε>0 is a small parameter. The unique solvability of the perturbed problem and estimates of it’s solution are obtained. The convergence of uε as ε→0 to the solution of the unperturbed problem is proved. Boundary layer is not appeared.

Keywords: Parabolic equation, boundary–value problem, small parameter in the boundary condition, Hölder space, existence, uniqueness, coercive estimates, convergence of the solution

DOI: 10.3233/ASY-211744

Journal: Asymptotic Analysis, vol. 130, no. 1-2, pp. 53-87, 2022