A5016610845- Mathematical Biology Tumor Growth
- Gene Regulatory Network Analysis
- Advanced Mathematical Modeling in Engineering
- Cellular Mechanics and Interactions
- Differential Equations and Numerical Methods
- Stability and Controllability of Differential Equations
- Numerical methods for differential equations
- Advanced Numerical Methods in Computational Mathematics
- Energy Efficient Wireless Sensor Networks
- Nonlinear Differential Equations Analysis
- Distributed Control Multi-Agent Systems
- Nonlinear Dynamics and Pattern Formation
- Differential Equations and Boundary Problems
- Fractional Differential Equations Solutions
- advanced mathematical theories
- Numerical methods in inverse problems
- Chromosomal and Genetic Variations
- Congenital heart defects research
- Advanced Mathematical Physics Problems
- Opinion Dynamics and Social Influence
- Developmental Biology and Gene Regulation
Tokyo Medical and Dental University
2009-2019
Osaka University
1999-2008
We construct the global bounded solutionsand attractors of a parabolic-parabolic chemotaxis-growth systemin two- and three-dimensional smooth domains.We derive new $L_p$ $H^2$ uniform estimates for these solutions.We then absorbing sets attractorsfor dynamical systems generated by also show existence exponential attractorsby applying theorem Eden-Foias-Nicolaenko-Temam.
Taking into account requirements of sensor networks, we need fully-distributed and self-organising control mechanisms which are scalable to the size a network, robust failures nodes, adaptive different dynamically changing topology changes in wireless communication environment. To accomplish this goal, our research group focuses on behaviour biological systems, inherently scalable, robust. In paper, first verify practicality adopting reaction-diffusion equation, explains emergence patterns...
We discuss an identification problem of a single point source for three-dimensional scalar wave equation. In this problem, the location and magnitude are assumed to be unknown. The moves in compact region, changes with time. As given data, we use observed values retarded potential its derivatives obtained at observation For propose direct method source. Our consists only methods linear algebra, though is formulated by partial differential Numerical examples also illustrate effectiveness our method.
In this paper we continue systematic study of the dimension estimate global attractor for chemotaxis-growth system. Using nonnegativity solu-tions manage significantly to improve estimates with respect chemotactic parameter.
We study the global existence of solutions to an $n$-dimensional parabolic-parabolic system for chemotaxis with logistic-type growth. introduce superlinear production a chemoattractant. then show in $L_p$ space $( p > n )$ under certain relations between degradation and orders.
We study fully discrete approximation of quasilinear parabolic systems. Presenting a full discretization scheme based on the Galerkin and Runge-Kutta methods, we establish stability error estimate by means semigroup method. First our results are stated for chemotaxis-growth system arising in biology, then those generalized to abstract evolution equations.
We study the global existence of solutions to an n-dimensional parabolic-parabolic system for chemotaxis with a subquadratic degradation. introduce sublinear production chemoattractant. then show in Lp space (p > n) under certain relations between degradation and orders.
Taking into account requirements of sensor networks, we need fully-distributed and self-organizing control mechanisms which are scalable to the size a network, robust failures nodes, adaptive different dynamically changing topology changes in wireless communication environment. To accomplish this goal, our research group focuses on behavior biological systems, inherently scalable, adaptive, robust. In paper, first verify practicality adopting reaction diffusion equation, explains emergence...
Abstract In this paper, we study an upper bound of the fractal dimension exponential attractor for chemotaxis–growth system in a two-dimensional domain. We apply technique given by Eden, Foias, Nicolaenko and Temam. Our results show that is estimated polynomial order with respect to chemotactic coefficient equation similar our preceding papers.
We study a finite-element approximation of the chemotaxis-growth system. establish dimension estimate global attractors for approximate systems. Our results show that estimates are uniform with respect to discretization parameter and polynomial order chemotactic coefficient in equation.We especially emphasize that, this is just same (polynomial) as original system obtained preceding papers [Adv.Math.Sci.Appl. Part I II].