HAMAMUKI, Nao
 Position
 Associate Professor
 Organization
 Department of Mathematics
 Research Interest
 Partial Differential Equations
 Research Activities

My major research topic is the study of nonlinear partial differential equations, especially evolution equations such as HamiltonJacobi equations and curvature flow equations which appear in materials science and describe a motion of a surface (an interface) separated by two different phases of matter.
On the basis of the theory of viscosity solutions, which is a notion of weak solutions for differential equations, I aim at introducing a suitable notion of solutions, establishing unique existence of solutions to the initial value problem and tracking the asymptotic behavior of solutions to give mathematical foundations to such nonlinear equations.
My current interests include a multifaceted understanding of phenomena via the limit process; for instance, finding a connection between a discrete/continuum problem and a microscopic/macroscopic model (homogenization). I will be glad if we could make links among various research fields through mathematics and find applications to new fields.
 Papers:
 Keywords
 HamiltonJacobi equation, Level set method, Maximum principle/Comparison principle, Viscosity solution
[1] Y. Giga, N. Hamamuki,
HamiltonJacobi equations with discontinuous source terms,
Comm. Partial Differential Equations 38 (2013), no. 2, 199–243.
[2] N. Hamamuki,
Asymptotically selfsimilar solutions to curvature flow equations with prescribed contact angle and their applications to groove profiles due to evaporationcondensation,
Adv. Differential Equations 19 (2014), no. 3–4, 317–358.
[3] Y. Giga, N. Hamamuki, A. Nakayasu,
Eikonal equations in metric spaces,
Trans. Amer. Math. Soc. 367 (2015), 49–66.