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This paper characterizes the dynamics of the positive solutions of
a class of sublinear parabolic cooperative systems whose analysis is
imperative for ascertaining the dynamics of wider classes of… (More)

Abstract In this paper we analyze the interplay between the most classical laws of Population Dynamics, Malthus versus Verhulst, in a class of sublinear cooperative parabolic systems, where, much… (More)

Abstract This paper is devoted to some aspects of well-posedness of the Cauchy problem (the CP, for short) for a quasilinear degenerate fourth-order parabolic thin film equation (the TFE-4) (0.1) u t… (More)

Fundamental global similarity solutions of the standard form
$$
u_\gamma(x,t) = t^{-\alpha_\gamma}
f_\gamma(y),\,\,\mbox{with the rescaled variable}\,\,\,
y= x/{t^{\beta_\gamma}}, \,\,… (More)

Solutions of the stationary semilinear Cahn-Hilliard-type equation −Δ2u−u−Δ(|u|p−1u)=0in RN,with p>1,$$-\Delta^{2} u - u -\Delta\bigl(|u|^{p-1}u\bigr)=0 \quad \mbox{in }\mathbb{R}^{N}, \mbox{with }… (More)

Fourth-order semilinear parabolic equations of the Cahn--Hilliard-type (01) u_t + \D^2 u = \g u \pm \D (|u|^{p-1}u) in \Omega \times \re_+, are considered in a smooth bounded domain $\O \subset \ren$… (More)

Abstract An approach to some “optimal” (more precisely, non-improvable) regularity of solutions of the thin film equation u t = − ∇ ⋅ ( | u | n ∇ Δ u ) in R N × R + , u ( x , 0 ) = u 0 ( x ) in R N ,… (More)

As the main problem, the bi-Laplace equation, being a model from fracture mechanics/elasticity, $\D^2 u=0 \quad (\D=D_x^2+D_y^2)$ in a bounded domain $\O \subset \re^2$, with inhomogeneous Dirichlet… (More)

Solutions of the stationary semilinear Cahn--Hilliard equation
-\Delta^2 u - u -\Delta(|u|^{p-1}u)=0 in R^N, with p>1, which are exponentially decaying at infinity, are studied. Using the Mounting… (More)

During the year 2009/2010 I was principally working on 3 different problems in collaboration with 4 different people, 3 of them working in Pisa and one in Parma. Those works led to 3 scientific… (More)