Mathematical analysis for nonlinear parabolic equations with degeneracy and mathematical models of grain boundary motion

2016 Fiscal Year Final Research Report

• Project/Area Number: 25800086
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical analysis
• Research Institution: Oita University (2016); SALESIAN POLYTECHNIC (2013-2015)
• Principal Investigator: Watanabe Hiroshi 大分大学, 工学部, 准教授 (30609912)
• Research Collaborator: SHIRAKAWA Ken ; Salvador Moll
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 退化放物型方程式 / 適切性 / エントロピー解 / 非局所量 / 結晶粒界現象 / 変分不等式 / エネルギー消散性 / 時間大域的挙動

Outline of Final Research Achievements

First purpose of the research is to study about the construction of well-posedness theory for systems of strongly degenerate parabolic equations. In fact, we clarify well-posedness for single strongly degenerate parabolic equations with variable coefficients. Moreover, we show well-posedness for systems of it coupling by means of nonlocal quantities.
Second purpose of the research is to show the solvability for the mathematical models which are described by grain boundary motion under various situations. I fact, we show the solvability of the model with degenerate coefficients, solidification effect and heat exchanges. Moreover, we characterize the large time behavior of the solutions.

Free Research Field

非線形偏微分方程式論