9 citations · 29 across the 16 of their papers we have counts for
16 papers
Remarks on some quasi-linear fourth order parabolic equations arising in mathematical physics
Francesco Fanelli, Rafael Granero-Belinchón, Martina Magliocca +1
This note proves existence and uniqueness of strong solutions to a broad class of fourth-order quasi-linear parabolic equations in the class of Wiener spaces. It improves upon prev…
A new asymptotic model of multilayer tumor growth
Rafael Granero-Belinchón, Martina Magliocca
In this paper we study the growth of a tumor colony of multilayer type and focus on how the tumor grows from a near flat (when compared to the length of the tumor as, for instance,…
Quasi-linear parabolic equations having a superlinear gradient term which depends on the solution
Andrea Dall'Aglio, Martina Magliocca, Sergio Segura de León
In this paper, we study existence and regularity for solutions to parabolic equations having a superlinear lower order term depending on both the solution and its gradient. Two dif…
Traveling Motility of Actin Lamellar Fragments Under spontaneous symmetry breaking
Claudia García, Martina Magliocca, Nicolas Meunier
Cell motility is connected to the spontaneous symmetry breaking of a circular shape. In https://doi.org/10.1103/PhysRevLett.110.078102, Blanch-Mercader and Casademunt perfomed a no…
New functional inequalities with applications to the arctan-fast diffusion equation
Rafael Granero-Belinchón, Martina Magliocca, Alejandro Ortega
In this paper, we prove a couple of new nonlinear functional inequalities of Sobolev type akin to the logarithmic Sobolev inequality. In particular, one of the inequalities reads $…
Global existence for certain fourth order evolution equations
Rafael Granero-Belinchón, Martina Magliocca
In this paper we establish three global in time results for two fourth order nonlinear parabolic equations. The first of such equations involves the Hessian and appears in epitaxia…
A nonlocal equation describing tumor growth
Rafael Granero-Belinchón, Martina Magliocca
Cancer is a very complex phenomenon that involves many different scales and situations. In this paper we consider a free boundary problem describing the evolution of a tumor colony…
Traveling wave solution for a coupled incompressible Darcy's free boundary problem with surface tension
Thomas Alazard, Martina Magliocca, Nicolas Meunier
We study an incompressible Darcy's free boundary problem, recently introduced in [22]. Our goal is to prove the existence of non-trivial traveling wave solutions and thus validate…
On a fourth order equation describing single-component film models
Martina Magliocca
We study existence results for a fourth order problem describing single-component film models assuming initial data in Wiener spaces.
On some parabolic equations involving superlinear singular gradient terms
Martina Magliocca, Francescantonio Oliva
In this paper we prove existence of nonnegative solutions to parabolic Cauchy-Dirichlet problems with superlinear gradient terms which are possibly singular. The model equation is…
Regularizing effects concerning elliptic equations with a superlinear gradient term
Marta Latorre Balado, Martina Magliocca, Sergio Segura de León
We consider the homogeneous Dirichlet problem for an elliptic equation driven by a linear operator with discontinuous coefficients and having a subquadratic gradient term. This gra…
Global existence and decay to equilibrium for some crystal surface models
Rafael Granero-Belinchón, Martina Magliocca
In this paper we study the large time behavior of the solutions to the following nonlinear fourth-order equations Thes…
Regularizing effect and decay results for a parabolic problem with repulsive superlinear first order terms
Martina Magliocca
We want to analyse both regularizing effect and long, short time decay concerning parabolic Cauchy-Dirichlet problems of the type \begin{equation*} \begin{cases} \begin{array}{ll}…
Comparison results for unbounded solutions for a parabolic Cauchy-Dirichlet problem with superlinear gradient growth
Tommaso Leonori, Martina Magliocca
In this paper we deal with uniqueness of solutions to the following problem \[ \begin{cases} \begin{split} & u_t-Δ_p u=H(t,x,\nabla u) &\quad \text{in}\quad Q_T,\\ & u (t,x) =0 &\q…
Local and global time decay for parabolic equations with super linear first order terms
Martina Magliocca, Alessio Porretta
We study a class of parabolic equations having first order terms with superlinear (and subquadratic) growth. The model problem is the so-called viscous Hamilton-Jacobi equation wit…
Existence results for a Cauchy-Dirichlet parabolic problem with a repulsive gradient term
Martina Magliocca
We study the existence of solutions of a nonlinear parabolic problem of Cauchy-Dirichlet type having a lower order term which depends on the gradient. The model we have in mind is…