Zobrazeno 1 - 10
of 46
pro vyhledávání: '"Thomas Duyckaerts"'
Autor:
Wei Dai, Thomas Duyckaerts
Publikováno v:
Journal of Evolution Equations. 21:4703-4750
In this paper, we prove the existence of a countable family of regular spherically symmetric self-similar solutions to focusing energy-supercritical semi-linear wave equations $$\begin{aligned} \partial _{tt}u-\Delta u=|u|^{p-1}u \qquad \text {in} \,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::abe31746afe2f4ff67565cc20c5e8cd6
https://doi.org/10.1007/s00028-021-00730-1
https://doi.org/10.1007/s00028-021-00730-1
Publikováno v:
The Journal of Geometric Analysis. 31:7036-7074
We consider the energy-critical focusing wave equation in space dimension $$N\ge 3$$ . The equation has a nonzero radial stationary solution W, which is unique up to scaling and sign change. It is conjectured (soliton resolution) that any radial, bou
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cc7de085c6e235c04e9d76cff82ead26
https://doi.org/10.1007/s12220-020-00591-z
https://doi.org/10.1007/s12220-020-00591-z
Autor:
Thomas Duyckaerts, David Lafontaine
Publikováno v:
Revista Matemática Iberoamericana
Revista Matemática Iberoamericana, 2022, 38 (2), pp.659-703. ⟨10.4171/RMI/1290⟩
Revista Matemática Iberoamericana, 2022, 38 (2), pp.659-703. ⟨10.4171/RMI/1290⟩
We show that the solutions of the three-dimensional critical defocusing nonlinear wave equation with Neumann boundary conditions outside a ball and radial initial data scatter. This is to our knowledge the first result of scattering for a nonlinear w
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::23e107320322ecf7ad1f32eb51adb947
https://hal.science/hal-03860699
https://hal.science/hal-03860699
Autor:
Wei Dai, Thomas Duyckaerts
Publikováno v:
Publ. Mat. 65, no. 1 (2021), 319-333
In this paper we study the existence of uniform a priori estimates for positive solutions to Navier problems of higher order Lane–Emden equations \begin{equation}\label{0-0} (-\Delta)^{m}u(x)=u^{p}(x), \quad x\in\Omega, \end{equation} for all large
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f92f739191337d826fb8f8e363f83a2c
https://projecteuclid.org/euclid.pm/1607655919
https://projecteuclid.org/euclid.pm/1607655919
We study the dynamics of the focusing $3d$ cubic nonlinear Schr\"odinger equation in the exterior of a strictly convex obstacle at the mass-energy threshold, namely, when $ E_{\Omega}[u_0] M_{\Omega}[u_0] = E_{\R^3}[Q] M_{\R^3}[Q] $ and $ \left\| \na
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::40de34ee13c13d4651e92313582f2eaa
http://arxiv.org/abs/2010.07724
http://arxiv.org/abs/2010.07724
We consider resonances associated with excited eigenvalues of the cavity of a general Helmholtz resonator with straight neck. Under the assumption that the neck stays away from the nodal set of the corresponding eigenstate, we generalise the optimal
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e3b971181ac3fec1e1bd4346276359ac
http://hdl.handle.net/11585/796898
http://hdl.handle.net/11585/796898
By definition, the exterior asymptotic energy of a solution to a wave equation on $${\mathbb {R}}^{1+N}$$ is the sum of the limits as $$t\rightarrow \pm \infty $$ of the energy in the the exterior $$\{|x|>|t|\}$$ of the wave cone. In our previous wor
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::07390657c1ab250e103b7e7c9e89d84b
http://arxiv.org/abs/1912.07658
http://arxiv.org/abs/1912.07658
Universality of Blow up Profile for Small Blow up Solutions to the Energy Critical Wave Map Equation
Publikováno v:
International Mathematics Research Notices. 2018:6961-7025
In this paper we introduce the channel of energy argument to the study of energy critical wave maps into the sphere. More precisely, we prove a channel of energy type inequality for small energy wave maps, and as an application we show that for a wav
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9c774db11ab3eefd3e2ef631b5c6b567
https://doi.org/10.1093/imrn/rnx073
https://doi.org/10.1093/imrn/rnx073
Autor:
Thomas Duyckaerts, Tristan Roy
Publikováno v:
Bulletin de la Société mathématique de France. 145:503-573
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::bdb3c029d76cf22416c47a7e69888e12
https://doi.org/10.24033/bsmf.2746
https://doi.org/10.24033/bsmf.2746
We provide an example of a normalized $L^{2}(\mathbb R)$ function $u$ such that its Wigner distribution $\mathcal W(u,u)$ has an integral $>1$ on the square $[0,a]\times[0,a]$ for a suitable choice of $a$. This provides a negative answer to a questio
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::21014d46d102c2c971d539fb0e1b73cb