Mathematical Analysis

Research Area “Mathematical Analysis” is devoted to theory on partial differential equations, theory of probability, functional analysis, dynamical systems and statistics.

For theory on partial differential equations, we study multi-dimensional traveling fronts appearing in reaction-diffusion models in physics, chemistry and biology. For theory of probability, we study stochastic partial differential equations and their discrete models.

	Prof. TANIGUCHI Masaharu E-mail: taniguchi-m＠(okayama-u.ac.jp) partial differential equations, theory of probability, functional analysis, dynamical systems, statistics Directory of Researchers 　Link to homepage

Pyramidal traveling fronts in the Allen–Cahn equations

For theory on partial differential equations, we study multi-dimensional traveling fronts in reaction-diffusion equations. We study V-form traveling fronts and pyramidal traveling fronts, axisymmetric traveling fronts, a traveling front whose cross section has a convex shape. Multi-dimensional traveling fronts describe propagation phenomena appearing in chemistry, physics and biology.

Quantum particles such as electrons are referred to as matter waves, and their motion does not conform to Newtonian mechanics.
Therefore, it is necessary to consider a different framework for understanding their motion, which is known as quantum mechanics.
The mathematical analysis of quantum mechanics, incorporating functional analysis, saw significant development in the latter half of the 20th century. However, many open research problems still remain.
I am particularly engaged in research on the mathematical analysis of the Schrödinger equation in electromagnetic fields.