Well-posedness and qualitative behaviour of the Mullins-Sekerka problem with ninety-degree angle boundary contact
| Autor: | Maximilian Rauchecker, Mathias Wilke, Helmut Abels |
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| Rok vydání: | 2021 |
| Předmět: |
ddc:510
Trace (linear algebra) General Mathematics 010102 general mathematics Mathematical analysis Boundary (topology) Motion (geometry) 510 Mathematik Space (mathematics) 01 natural sciences Exponential function 010101 applied mathematics Nonlinear system Mathematics - Analysis of PDEs Linearization FOS: Mathematics Contraction mapping 0101 mathematics Analysis of PDEs (math.AP) Mathematics |
| DOI: | 10.25673/108764 |
| Popis: | We show local well-posedness for the Mullins-Sekerka system with ninety degree angle boundary contact. We will describe the motion of the moving interface by a height function over a fixed reference surface. Using the theory of maximal regularity together with a linearization of the equations and a localization argument we will prove well-posedness of the full nonlinear problem via the contraction mapping principle. Here one difficulty lies in choosing the right space for the Neumann trace of the height function and showing maximal $L_p-L_q$-regularity for the linear problem. In the second part we show that solutions starting close to certain equilibria exist globally in time, are stable, and converge to an equilibrium solution at an exponential rate. Comment: 36 pages |
| Databáze: | OpenAIRE |
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