| Co-Investigator(Kenkyū-buntansha) |
石井 仁司 津田塾大学, 数学・計算機科学研究所, 研究員 (70102887)
利根川 吉廣 東京工業大学, 理学院, 教授 (80296748)
山本 昌宏 東京大学, 大学院数理科学研究科, 教授 (50182647)
神保 秀一 北海道大学, 理学研究院, 教授 (80201565)
久保 英夫 北海道大学, 理学研究院, 教授 (50283346)
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| Budget Amount *help |
¥155,740,000 (Direct Cost: ¥119,800,000、Indirect Cost: ¥35,940,000)
Fiscal Year 2018: ¥36,270,000 (Direct Cost: ¥27,900,000、Indirect Cost: ¥8,370,000)
Fiscal Year 2017: ¥35,620,000 (Direct Cost: ¥27,400,000、Indirect Cost: ¥8,220,000)
Fiscal Year 2016: ¥36,660,000 (Direct Cost: ¥28,200,000、Indirect Cost: ¥8,460,000)
Fiscal Year 2015: ¥35,620,000 (Direct Cost: ¥27,400,000、Indirect Cost: ¥8,220,000)
Fiscal Year 2014: ¥11,570,000 (Direct Cost: ¥8,900,000、Indirect Cost: ¥2,670,000)
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| Outline of Final Research Achievements |
We prove the existence and the uniqueness of a solution and clarify its behavior for evolution equations mainly nonlinear diffusion equations describing evolution of patterns and shapes like crystal growth phenomena. We introduce new notions of a solution which allows shape with singularities for equations having singular structure. We thus establish foundation of mathematical analysis which easily describes real phenomena. Based on these fundamental results, we are able to numerically calculate phenomena which had been difficult to calculate, for example, phenomena of colliding spirals on surfaces of crystals.
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