Zobrazeno 1 - 10
of 57
pro vyhledávání: '"Dı́az, Jesús Ildefonso"'
We pass to the limit in the homogenization of an optimal control problem associated with a parabolic equation with a dynamic boundary condition. New unexpected terms appear due to the critical scale.
Externí odkaz:
http://arxiv.org/abs/2406.18712
Autor:
Bégout, Pascal, Díaz, Jesús Ildefonso
Publikováno v:
Journal of Mathematical Analysis and Applications, 2024, 538 (1), pp.128329
We consider the damped nonlinear Schr\''{o}dinger equation with saturation: i.e., the complex evolution equation contains in its left hand side, besides the potential term $V(x)u,$ a nonlinear term of the form $\mathrm{i}\mu u(t,x)/|u(t,x)|$ for a gi
Externí odkaz:
http://arxiv.org/abs/2404.06811
We show that the classical strong maximum principle, concerning positive supersolutions of linear elliptic equations vanishing on the boundary of the domain $\Omega $ can be extended, under suitable conditions, to the case in which the forcing term $
Externí odkaz:
http://arxiv.org/abs/2308.02626
In this paper we study existence, uniqueness, and integrability of solutions to the Dirichlet problem $-\mathrm{div}( M(x) \nabla u ) = -\mathrm{div} (E(x) u) + f$ in a bounded domain of $\mathbb R^N$ with $N \ge 3$. We are particularly interested in
Externí odkaz:
http://arxiv.org/abs/2211.10122
Autor:
Bégout, Pascal, Díaz, Jesús Ildefonso
Publikováno v:
Advances in Differential Equations, 2023, 28 (3-4), pp.311-340
This paper completes some previous studies by several authors on the finite time extinction for nonlinear Schr{\"o}dinger equation when the nonlinear damping term corresponds to the limit cases of some ``saturating non-Kerr law'' $F(|u|^2)u=\frac{a}{
Externí odkaz:
http://arxiv.org/abs/2210.04493
Autor:
Díaz, Gregorio, Díaz, Jesús Ildefonso
We consider a class of one-dimensional nonlinear stochastic parabolic problems associated with Sellers and Budyko diffusive energy balance climate models with a Legendre weighted diffusion and an additive cylindrical Wiener processes forcing. Our res
Externí odkaz:
http://arxiv.org/abs/2111.10801
Autor:
Bégout, Pascal, Díaz, Jesús Ildefonso
Publikováno v:
Journal of Differential Equations, 2022, 308, pp.252-285
We present some sharper finite extinction time results for solutions of a class of damped nonlinear Schr{\"o}dinger equations when the nonlinear damping term corresponds to the limit cases of some ``saturating non-Kerr law'' $F(|u|^2)u=\frac{a}{\vare
Externí odkaz:
http://arxiv.org/abs/2111.10136
Finite time extinction for the strongly damped nonlinear Schr{\'o}dinger equation in bounded domains
Autor:
Bégout, Pascal, Díaz, Jesús Ildefonso
Publikováno v:
Journal of Differential Equations, Elsevier, 2020, 268 (7), pp.4029-4058
We prove the \textit{finite time extinction property} $(u(t)\equiv 0$ on $\Omega$ for any $t\ge T_\star,$ for some $T_\star>0)$ for solutions of the nonlinear Schr\"{o}dinger problem ${\rm i} u_t+\Delta u+a|u|^{-(1-m)}u=f(t,x),$ on a bounded domain $
Externí odkaz:
http://arxiv.org/abs/2003.08105
We consider a slow diffusion equation with a singular quenching term, extending the mathematical treatment made in 1992 by B. Kawohl and R. Kersner for the one-dimensional case. Besides the existence of a very weak solution, we prove some pointwise g
Externí odkaz:
http://arxiv.org/abs/2001.10193
Publikováno v:
Annales de l'Institut Henri Poincar{\'{e}} C, Analyse non lin{\'{e}}aire, 38 (2), 2021
In this paper we obtain comparison results for the quasilinear equation $-\Delta_{p,x} u - u_{yy} = f$ with homogeneous Dirichlet boundary conditions by Steiner rearrangement in variable $x$, thus solving a long open problem. In fact, we study a broa
Externí odkaz:
http://arxiv.org/abs/1912.02080