Zobrazeno 1 - 10
of 78
pro vyhledávání: '"Thierry Cazenave"'
Autor:
Zheng Han, Thierry Cazenave
Publikováno v:
Discrete and Continuous Dynamical Systems-Series A
Discrete and Continuous Dynamical Systems-Series A, American Institute of Mathematical Sciences, 2020, 40 (8), pp.4801-4819. ⟨10.3934/dcds.2020202⟩
Discrete and Continuous Dynamical Systems-Series A, American Institute of Mathematical Sciences, 2020, 40 (8), pp.4801-4819. ⟨10.3934/dcds.2020202⟩
We study the time-asymptotic behavior of solutions of the Schrodinger equation with nonlinear dissipation \begin{document}$ \begin{equation*} \partial _t u = i \Delta u + \lambda |u|^\alpha u \end{equation*} $\end{document} in \begin{document}$ {\mat
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c8ec6b0b17376d0cadf16dd87a2d6e07
https://doi.org/10.3934/dcds.2020202
https://doi.org/10.3934/dcds.2020202
Autor:
Ivan Naumkin, Thierry Cazenave
Publikováno v:
Discrete and Continuous Dynamical Systems-Series S
Discrete and Continuous Dynamical Systems-Series S, American Institute of Mathematical Sciences, 2021, 14 (5), pp.1649-1672. ⟨10.3934/dcdss.2020448⟩
Discrete and Continuous Dynamical Systems-Series S, American Institute of Mathematical Sciences, 2021, 14 (5), pp.1649-1672. ⟨10.3934/dcdss.2020448⟩
Given any \begin{document}$ \mu _1, \mu _2\in {\mathbb C} $\end{document} and \begin{document}$ \alpha >0 $\end{document} , we prove the local existence of arbitrarily smooth solutions of the nonlinear Klein-Gordon equation \begin{document}$ \partial
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d0aaa675f31961fac70b39535c8d7cdd
https://hal.archives-ouvertes.fr/hal-02228045
https://hal.archives-ouvertes.fr/hal-02228045
Publikováno v:
Nonlinear Analysis: Theory, Methods and Applications
Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2021, 205, pp.112243. ⟨10.1016/j.na.2020.112243⟩
Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2021, 205, pp.112243. ⟨10.1016/j.na.2020.112243⟩
International audience; We consider the Schr\"odinger equation with nonlinear dissipation \begin{equation*} i \partial _t u +\Delta u=\lambda|u|^{\alpha}u \end{equation*} in ${\mathbb R}^N $, $N\geq1$, where $\lambda\in {\mathbb C} $ with $\Im\lambda
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0a9044ed57835f0352c914313cfe06e4
http://arxiv.org/abs/2007.13697
http://arxiv.org/abs/2007.13697
Publikováno v:
ESAIM: Control, Optimisation and Calculus of Variations
ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2020, 26, pp.126. ⟨10.1051/cocv/2020082⟩
ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2020, 26, pp.126. ⟨10.1051/cocv/2020082⟩
We study the existence of sign-changing solutions to the nonlinear heat equation ∂tu = Δu + |u|αu on ℝN, N ≥ 3, with 2/N−2 <α<α0, where α0=4/N−4+2√N−1 ∈ (2/N−2,4/N−2), which are singular at x = 0 on an interval of time. In pa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3031ffe7518107bf88af9e1d9382a3b9
https://hal.archives-ouvertes.fr/hal-02893405/document
https://hal.archives-ouvertes.fr/hal-02893405/document
Publikováno v:
Journal of Dynamics and Differential Equations
Journal of Dynamics and Differential Equations, Springer Verlag, 2021, 33 (2), pp.941-960. ⟨10.1007/s10884-020-09841-8⟩
Journal of Dynamics and Differential Equations, Springer Verlag, 2021, 33 (2), pp.941-960. ⟨10.1007/s10884-020-09841-8⟩
We consider the nonlinear Schrodinger equation on $${\mathbb R}^N $$ , $$N\ge 1$$ , $$\begin{aligned} \partial _t u = i \varDelta u + \lambda | u |^\alpha u \end{aligned}$$ with $$\lambda \in {\mathbb C}$$ and $$\mathfrak {R}\lambda >0$$ , for $$H^1$
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::31c8142b702b0ffc685898d08d8d3f49
http://arxiv.org/abs/1906.02983
http://arxiv.org/abs/1906.02983
Autor:
Thierry Cazenave, Seifeddine Snoussi
Publikováno v:
Partial Differential Equations Arising from Physics and Geometry
Partial Differential Equations Arising from Physics and Geometry, 450, Cambridge University Press, 2019, London Mathematical Society Lecture Note Series, 9781108367639. ⟨10.1017/9781108367639.004⟩
Partial Differential Equations Arising from Physics and Geometry, 450, Cambridge University Press, 2019, London Mathematical Society Lecture Note Series, 9781108367639. ⟨10.1017/9781108367639.004⟩
International audience; In this article, we review finite-time blowup criteria for the family of complex Ginzburg-Landau equations $u_t = e^{ i\theta } [\Delta u + |u|^\alpha u] + \gamma u$ on ${\mathbb R}^N $, where $0 \le \theta \le \frac {\pi } {2
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f8d03131f206afae34ee69329c7ddb49
https://doi.org/10.1017/9781108367639.004
https://doi.org/10.1017/9781108367639.004
Publikováno v:
Advanced Nonlinear Studies
Advanced Nonlinear Studies, Walter de Gruyter GmbH, 2019, ⟨10.1515/ans-2019-2059⟩
Advanced Nonlinear Studies, Walter de Gruyter GmbH, 2019, ⟨10.1515/ans-2019-2059⟩
We prove that any sufficiently differentiable space-like hypersurface of ℝ 1 + N {{\mathbb{R}}^{1+N}} coincides locally around any of its points with the blow-up surface of a finite-energy solution of the focusing nonlinear wave equation ∂ t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6a601353c63e0977c3e080536b9f635d
https://hal.archives-ouvertes.fr/hal-02093906
https://hal.archives-ouvertes.fr/hal-02093906
Publikováno v:
Dynamics of Partial Differential Equations
Dynamics of Partial Differential Equations, International Press, 2019, 16 (2), pp.151-183. ⟨10.4310/DPDE.2019.v16.n2.a3⟩
Dynamics of Partial Differential Equations, International Press, 2019, 16 (2), pp.151-183. ⟨10.4310/DPDE.2019.v16.n2.a3⟩
International audience; We consider the nonlinear heat equation $u_t = \Delta u + |u|^\alpha u$ with $\alpha >0$, either on ${\mathbb R}^N $, $N\ge 1$, or on a bounded domain with Dirichlet boundary conditions. We prove that in the Sobolev subcritica
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b45d47410acec759b325699e250c3385
https://hal.archives-ouvertes.fr/hal-01826926
https://hal.archives-ouvertes.fr/hal-01826926
Publikováno v:
Discrete and Continuous Dynamical Systems-Series A
Discrete and Continuous Dynamical Systems-Series A, American Institute of Mathematical Sciences, 2019, 39 (2), pp.1171-1183. ⟨10.3934/dcds.2019050⟩
Discrete and Continuous Dynamical Systems-Series A, American Institute of Mathematical Sciences, 2019, 39 (2), pp.1171-1183. ⟨10.3934/dcds.2019050⟩
International audience; We consider the nonlinear Schr\"odinger equation \[ u_t = i \Delta u + | u |^\alpha u \quad \mbox{on ${\mathbb R}^N $, $\alpha>0$,} \] for $H^1$-subcritical or critical nonlinearities: $(N-2) \alpha \le 4$. Under the additiona
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ed817d51466c5eec4b2c6c4a413f84d6
https://hal.archives-ouvertes.fr/hal-01826927
https://hal.archives-ouvertes.fr/hal-01826927
We consider the focusing energy subcritical nonlinear wave equation ∂ t t u − Δ u = | u | p − 1 u in R N , N ≥ 1 . Given any compact set K ⊂ R N , we construct finite energy solutions which blow up at t = 0 exactly on K. The construction i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::21dd1c2259d2448d7df1e8fe0ca0207c
http://arxiv.org/abs/1812.03949
http://arxiv.org/abs/1812.03949