Critical Phenomena in Nonlinear Partial Differential Equations, Harmonic Analysis, and Functional Inequalities, Vol. 1

Jun-ichi Segata is a currently Professor at Faculty of Mathematics, Kyushu University. He previously held positions at Fukuoka University of Education, and Tohoku University. He is studying on the nonlinear dispersive and hyperbolic PDEs via the harmonic analysis approach. He earned Ph.D in Mathematics at Kyushu University in 2005.  Hiroshi Takeda is a Professor  at Fukuoka University. He worked at Tohoku University and Fukuoka Institute of Technology. His research field is the nonlinear hyperbolic PDEs from the point of view of long time behavior. He obtained  Ph.D at Tohoku University in 2010. Masashi Mizuno is an Associate Professor at Nihon University. His research interest is nonlinear analysis, regularity theory for nonlinear PDEs, geometric measure theory and its application, mathematical modeling for grain boundary motion. He earned Ph.D at Tohoku University.  Masakazu Yamamoto is an Associate Professor at Niigata University. He is studying on the drift–diffusion equation and nonlinear PDEs arising in the fluid mechanics. He obtained  Ph.D at Tohoku University.

• Preface.- Biographical Sketch and Academic Career of Takayoshi Ogawa.- Some consequences of the sharp Euclidean logarithmic Sobolev inequality with monomial weight.- Uniqueness of almost periodic-in-time solutions to the Boussinesq system in unbounded domains.- $L^p$ estimate of the heat equation on a bounded domain.- A note on strong instability of standing waves for nonlinear Schr¨odinger equations with double power nonlinearity.