5 papers
On the optimal decay rate of global solutions to the convection-diffusion equation with zero-mass initial data
Yi C. Huang, Ryunosuke Kusaba
We consider the optimal decay rate of global solutions to the convection-diffusion equation with zero-mass initial data. We establish an improved decay estimate of the global solut…
Remarks on the commutation relations between the Gauss--Weierstrass semigroup and monomial weights
Yi C. Huang, Ryunosuke Kusaba, Tohru Ozawa
We consider the commutation relations between the Gauss--Weierstrass semigroup on , generated by convolution with the complex Gaussian kernel, and monomial weights.…
Higher order asymptotic expansions for the convection-diffusion equation in the Fujita-subcritical case
Ryunosuke Kusaba
This paper is devoted to the asymptotic behavior of global solutions to the convection-diffusion equation in the Fujita-subcritical case. We improve the result by Zuazua (1993) and…
Asymptotic behavior of global solutions to the complex Ginzburg--Landau type equation in the super Fujita-critical case
Ryunosuke Kusaba, Tohru Ozawa
We present weighted estimates and higher order asymptotic expansions of global solutions to the complex Ginzburg--Landau (CGL) type equation in the super Fujita-critical case. Our…
Weighted estimates and large time behavior of small amplitude solutions to the semilinear heat equation
Ryunosuke Kusaba, Tohru Ozawa
We present a new method to obtain weighted -estimates of global solutions to the Cauchy problem for the semilinear heat equation with a simple power of super-critical Fujita…