| Budget Amount *help |
¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2014: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2013: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2012: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2011: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
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| Outline of Final Research Achievements |
The aim of this research project is to consider nonlinear problems related to interfacial motions and blow-up phenomena.The methods are based on scaling related to the symmetry of the equation and on the theory of infinite dimensional dynamical systems. The following results have been obtained:(1)We studied nonlinear heat equations with power nonlinearity multiplied by a spatial inhomogeneous coefficient, which has zero points in the domain.We have given several conditions to determine blow-up point point.(2)We consider the Cauchy problem for a system of parabolic equations which is derived from a complex-valued equation with a quadratic nonlinearity. Global dynamics and blow-up phenomena was considered.(3)We have succeeded in determining all possible type of the behavior of a free boundary problem of a curvature-dependent motion of a curve, by applying new ``extended'' intersetion number principle. The results for asymptotic behavior and convexity are also established.
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