4 papers · 1 filter
Stochastic diffusive energy balance climate model with a multiplicative noise modeling the Solar variability
Gregorio Díaz, Jesús Ildefonso Díaz
We prove the existence, uniqueness, and comparison of solutions for a nonlinear stochastic parabolic partial differential equation that includes the Solar variability in terms of a…
Solutions with expanding compact support of saturated Schr{ö}dinger equations: self-similar solutions
Pascal Bégout, Jesus Ildefonso Diaz
We prove the existence of solutions \(u(t,x)\) of the Schr{ö}dinger equation with a saturation nonlinear term \((u/|u|)\) having compact support, for each \(t>0,\) that expands wit…
New unexpected limit operators for homogenizing optimal control parabolic problems with dynamic reaction flow on the boundary of critically scaled particles
Jesus Ildefonso Diaz, Alexander V. Podolskiy, Tatiana A. Shaposhnikova
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…
Flat solutions of some non-Lipschitz autonomous semilinear equations may be stable for
Jesús Ildefonso Díaz, Jesús Hernández, Yavdat Il'yasov
We prove that flat ground state solutions ( minimizing the energy and with gradient vanishing on the boundary of the domain) of the Dirichlet problem associated to some semil…