108 citations · 419 across the 35 of their papers we have counts for
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Explicit blowing up solutions for a higher order parabolic equation with Hessian nonlinearity
Carlos Escudero
In this work we consider a nonlinear parabolic higher order partial differential equation that has been proposed as a model for epitaxial growth. This equation possesses both globa…
Polyharmonic Hessian equations in
Pedro Balodis, Carlos Escudero
This work is focused on the study of the nonlinear elliptic higher order equation \begin{equation}\nonumber \left( -Δ\right)^m u = S_k[-u] + λf, \qquad x \in \mathbb{R}^N, \end{equ…
On polyharmonic regularizations of Hessian equations: Variational methods
Carlos Escudero
This work is devoted to the study of the boundary value problem \begin{eqnarray}\nonumber (-1)^αΔ^αu = (-1)^k S_k[u] + λf, \qquad x &\in& Ω\subset \mathbb{R}^N, \\ \nonumber u = \p…
Existence results for a fourth order partial differential equation arising in condensed matter physics
Carlos Escudero, Filippo Gazzola, Robert Hakl +2
We study a higher order parabolic partial differential equation that arises in the context of condensed matter physics. It is a fourth order semilinear equation whose nonlinearity…
Global existence versus blow-up results for a fourth order parabolic PDE involving the Hessian
Carlos Escudero, Filippo Gazzola, Ireneo Peral
We consider a partial differential equation that arises in the coarse-grained description of epitaxial growth processes. This is a parabolic equation whose evolution is governed by…
Kinetic theory and numerical simulations of two-species coagulation
Carlos Escudero, Fabricio Macia, Raul Toral +1
In this work we study the stochastic process of two-species coagulation. This process consists in the aggregation dynamics taking place in a ring. Particles and clusters of particl…