Regularity of Solutions to a Model Oblique Derivative Problem for Quasilinear Parabolic Systems with Nondiagonal Principal Matrices
| Autor: | Arina A. Arkhipova, G. V. Grishina |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Lateral surface
Plane (geometry) General Mathematics Weak solution 010102 general mathematics Mathematical analysis Boundary (topology) Parabolic cylinder function System of linear equations 01 natural sciences 010305 fluids & plasmas Matrix (mathematics) 0103 physical sciences Cylinder 0101 mathematics Mathematics |
| Zdroj: | Vestnik St. Petersburg University, Mathematics. 52:1-18 |
| ISSN: | 1934-7855 1063-4541 |
| Popis: | We consider quasilinear parabolic systems of equations with nondiagonal principal matrices. The oblique derivative of a solution is defined on the plane part of the lateral surface of a parabolic cylinder. We do not assume smoothness of the principal matrix and the boundary functions in the time variable and prove partial Holder continuity of a weak solution near the plane part of the lateral surface of the cylinder. Holder continuity of weak solutions to the correspondent linear problem is stated. A modification of the A(t)-caloric approximation method is applied to study the regularity of weak solutions. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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