Zobrazeno 1 - 10
of 25
pro vyhledávání: '"Kyouhei Wakasa"'
Publikováno v:
Journal of Differential Equations. 267:5165-5201
In this paper we consider the wave equations with power type nonlinearities including time-derivatives of unknown functions and their weakly coupled systems. We propose a framework of test function methods and give a simple proof of the derivation of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d3904b84cced56052f53249b1dcacba2
https://doi.org/10.1016/j.jde.2019.05.029
https://doi.org/10.1016/j.jde.2019.05.029
Autor:
Borislav Yordanov, Kyouhei Wakasa
Publikováno v:
Journal of Differential Equations. 266:5360-5376
We verify the critical case $p=p_0(n)$ of Strauss' conjecture (1981) concerning the blow-up of solutions to semilinear wave equations with variable coefficients in $\mathbf{R}^n$, where $n\geq 2$. The perturbations of Laplace operator are assumed to
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fd322043601e9e43d3b41e09135bc726
https://doi.org/10.1016/j.jde.2018.10.028
https://doi.org/10.1016/j.jde.2018.10.028
Autor:
Borislav Yordanov, Kyouhei Wakasa
Publikováno v:
Nonlinear Analysis. 180:67-74
We consider the Cauchy problem for semilinear wave equations with variable coefficients and time-dependent scattering damping in R n , where n ≥ 2 . It is expected that the critical exponent will be Strauss’ number p 0 ( n ) , which is also the o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::38fd85a792baa795f80f7dd9cd840558
https://doi.org/10.1016/j.na.2018.09.012
https://doi.org/10.1016/j.na.2018.09.012
In this paper we study the initial boundary value problem for two-dimensional semilinear wave equations with small data, in asymptotically Euclidean exterior domains. We prove that if $1
Comment: 24 pages
Comment: 24 pages
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1cecc2082c04d55f49947191a4af5f1b
http://arxiv.org/abs/2006.12192
http://arxiv.org/abs/2006.12192
In the present paper, we study the Cauchy problem for the wave equation with a time-dependent scale invariant damping term 2 1 + t ∂ t v and a cubic convolution ( | x | − γ ⁎ v 2 ) v with γ ∈ ( − 1 2 , 3 ) in three spatial dimension for i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::230ba1f0266ece5aa435d856e40c0da4
http://arxiv.org/abs/2003.10329
http://arxiv.org/abs/2003.10329
Autor:
Kyouhei Wakasa, Tomoyuki Tanaka
We consider the wave equation with a cubic convolution $\partial_t^2 u-\Delta u=(|x|^{-\gamma}*u^2)u$ in three space dimensions. Here, $0
Comment: 31 pages
Comment: 31 pages
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c9718624dbfa4422972de01e33dc508b
Autor:
Borislav Yordanov, Kyouhei Wakasa
Publikováno v:
Journal of Mathematical Analysis and Applications. 455:1317-1322
The energy decay problem is studied for the nonlinear dissipative wave equation in one space dimension. It is shown by Mochizuki and Motai [6] that the decay rate is at least logarithmic when the exponent of the nonlinearity is greater than one and l
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9187626df94d2f998137dd9c87e03eac
https://doi.org/10.1016/j.jmaa.2017.06.015
https://doi.org/10.1016/j.jmaa.2017.06.015
Autor:
Borislav Yordanov, Kyouhei Wakasa
Publikováno v:
Nonlinear Analysis: Theory, Methods & Applications. 152:183-195
The nonlinear wave equation $u_{tt}-\Delta u +|u_t|^{p-1}u_t=0$ is shown to be globally well-posed in the Sobolev spaces of radially symmetric functions $H^k_{\rm rad}({\bf R}^3)\times H^{k-1}_{\rm rad}({\bf R}^3)$ for all $p\geq 3$ and $k\geq 3$. Mo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7351830e7ad1e356caecb4b36f9fd5c8
https://doi.org/10.1016/j.na.2016.12.013
https://doi.org/10.1016/j.na.2016.12.013
In this paper, we study the initial value problem for semilinear wave equations with the time-dependent and scale-invariant damping in two dimensions. Similarly to the one dimensional case by Kato, Takamura and Wakasa in 2019, we obtain the lifespan
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4884590d36eb5d367b1f77fc30a306c9
http://arxiv.org/abs/1910.11692
http://arxiv.org/abs/1910.11692
In the present paper, we study small data blow-up of the semi-linear wave equation with a scattering dissipation term and a time-dependent mass term from the aspect of wave-like behavior. The Strauss type critical exponent is determined and blow-up r
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b39c0a0777a6c72c2c55d689cfc18655
http://arxiv.org/abs/1904.09574
http://arxiv.org/abs/1904.09574