arXiv subjects

Ryo Ikehata

Publications and source records attributed to Ryo Ikehata.

43 records · Page 3Linked to original sources

arXiv2016

Asymptotic profiles of solutions for structural damped wave equations

In this paper, we obtain several asymptotic profiles of solutions to the Cauchy problem for structurally damped wave equations $\partial_{t}^{2} u - Δu + ν(-Δ)^σ \partial_{t} u=0$, where $ν>0$ and $0< σ\le1$. Our result is the approximation formula of the solution by a constant multiple of a special function as $t \to \infty$, which states that the asymptotic profiles of the solutions are classified into $5$ patterns depending on the values $ν$ and $σ$.

math.AP↗

arXiv2016

Large time behaivor of global solutions to nonlinear wave equations with frictional and viscoelastic damping terms

In this paper, we study the Cauchy problem for a nonlinear wave equation with frictional and viscoelastic damping terms. As is pointed out by [8], in this combination, the frictional damping term is dominant for the viscoelastic one for the global dynamics of the linear equation. In this note we observe that if the initial data is small, the frictional damping term is again dominant even in the nonlinear equation case. In other words, our main result is diffusion phenomena: the solution is approximated by the heat kernel with a suitable constant. Our proof is based on several estimates for the corresponding linear equations.

math.AP↗

arXiv2016

Critical exponent for nonlinear wave equations with frictional and viscoelastic damping terms

In this paper, we study the Cauchy problem for a nonlinear wave equation with frictional and viscoelastic damping terms. Our aim is to obtain the threshold, to classify the global existence of solution for small data or the finite time blow-up pf the solution, with respect to the growth order of the nonlinearity.

math.AP↗

arXiv2016

Asymptotic profile of solutions to the linearized compressible Navier-Stokes flow

We consider the asymptotic behavior as time goes to infinity of the $L^{2}$-norm of the velocity of the linearized compressible Navier-Stokes equations in ${\bf R}^{n}$ ($n \geq 2$). As an application we shall study the optimality of the decay rate for the $L^{2}$-norm of the velocity by deriving the decay estimate from below as time goes to infinity.

math.AP↗

arXiv2015

Fast energy decay for wave equations with variable damping coefficients in the 1-D half line

We derive fast decay estimates of the total energy for wave equations with localized variable damping coefficients, which are dealt with in the one dimensional half line $(0,\infty)$. The variable damping coefficient vanishes near the boundary $x = 0$, and is effective critically near spatial infinity $x = \infty$.

math.AP↗

arXiv2015

Revisit on How to Derive Asymptotic Profiles to Some Evolution Equations

We consider the Cauchy problem in ${\bf R}^{n}$ for heat and damped wave equations. We derive asymptotic profiles to those solutions with weighted $L^{1,1}({\bf R}^{n})$ data by presenting a simple method.

math.AP↗

arXiv2014

Asymptotic Profiles for wave equations with strong damping

We consider the Cauchy problem in ${\bf R}^{n}$ for strongly damped wave equations. We derive asymptotic profiles of these solutions with weighted $L^{1,1}({\bf R}^{n})$ data by using a method introduced in [10].

math.AP↗