arXiv subjects

Ryôhei Kakizawa

Publications and source records attributed to Ryôhei Kakizawa.

4 recordsLinked to original sources

arXiv2010

Determining nodes for semilinear parabolic equations

We are concerned with the uniqueness of the asymptotic behavior of strong solutions of the initial-boundary value problem for general semilinear parabolic equations by the asymptotic behavior of these strong solutions on a finite set of an entire domain. More precisely, if the asymptotic behavior of a strong solution is known on an appropriate finite set, then the asymptotic behavior of a strong solution itself is entirely determined in a domain. We prove the above property by the energy method.

math.AP↗

arXiv2010

The initial value problem for motion of incompressible viscous and heat-conductive fluids in Banach spaces

We consider the abstract initial value problem for the system of evolution equations which describe motion of incompressible viscous and heat-conductive fluids in a bounded domain. It is difficulty of our problem that we do not neglect the viscous dissipation function in contrast to the Boussinesq approximation. This problem has uniquely a mild solution locally in time for general initial data, and globally in time for small initial data. Moreover, a mild solution of this problem can be a strong or classical solution under appropriate assumptions for initial data. We prove the above properties by the theory of analytic semigroups on Banach spaces.

math.AP↗

arXiv2010

The initial value problem for motion of micropolar fluids with heat conduction in Banach spaces

We consider the abstract initial value problem for the system of evolution equations which describe motion of micropolar fluids with heat conduction in a bounded domain. This problem has uniquely a mild solution locally in time for general initial data, and globally in time for small initial data. Moreover, a mild solution of this problem can be a strong or classical solution under appropriate assumptions for initial data. We prove the above properties by the theory of analytic semigroups on Banach spaces.

math.AP↗

arXiv2010

Global $L_{p}$-$L_{q}$ estimates for solutions to the third initial-boundary value problem for the heat equation in a bounded domain

We discuss the unique solvability of the third initial-boundary value problem for the heat equation in a bounded domain. This problem has uniquely a time-global solution in the anisotropic Sobolev space $W^{2,1}_{p,q}$ for any $1<p<\infty$, $1<q<\infty$. Moreover, exponentially weighted $L_{p}$-$L_{q}$ estimates for time-global solutions can be established. We prove the above properties by $L_{p}$ estimates for steady solutions to the heat equation, the theory of analytic semigroups on Banach spaces and the operator-valued Fourier multiplier theorem on UMD spaces.

math.AP↗