scholarly journals An irregular conjugation problem for the system of the parabolic equations in the holder space

2020 ◽  
Vol 11 (1) ◽  
pp. 36-44
Author(s):  
Zh. K. Dzhobulaeva ◽  
Keyword(s):  
Parabolic Equations ◽  
Conjugation Problem ◽  
Holder Space ◽  
Hölder Space

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

2021 ◽  
pp. 1-35
Author(s):  
Galina Bizhanova
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Parabolic Equation ◽  
Small Parameter ◽  
Unique Solvability ◽  
Time Derivative ◽  
Holder Space ◽  
Hölder Space ◽  
Space Solution ◽  
Unperturbed Problem

There is studied the Hölder space solution u ε of the problem for parabolic equation with the time derivative ε ∂ t u ε | 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 u ε as ε → 0 to the solution of the unperturbed problem is proved. Boundary layer is not appeared.

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