Instantaneous blow-up of solutions to a class of hyperbolic inequalities.
How parabolic free boundaries approximate hyperbolic fronts.
Uniqueness of solutions to degenerate elliptic problems with unbounded coefficients
Harnack inequality and heat kernel estimates for the Schrödinger operator with Hardy potential
In this preliminary Note we outline some results of the forthcoming paper [11], concerning positive solutions of the equation . A parabolic Harnack inequality is proved, which in particular implies a sharp two-sided estimate for the associated heat kernel. Our approach relies on the unitary equivalence of the Schrödinger operator with the opposite of the weighted Laplacian when .
Asymptotic stability properties for nonlinear diffusion Volterra equations
Si dimostra la stabilità asintotica uniforme dell'unico equilibrio non banale di un'equazione integrodifferenziale di Volterra con diffusione, soggetta a condizioni ai limiti di tipo Dirichlet.
On the asymptotic stability for abstract Volterra integro-differential equations
Si danno condizioni per la stabilità asintotica della soluzione nulla di una classe di equazioni integro-differenziali di Volterra in spazi di Banach.
Invariant Rectangles and Strongly Coupled Semilinear Parabolic.
Nonexistence of local solutions to semilinear partial differential inequalities
Blow-up of nonnegative solutions to quasilinear parabolic inequalities
We investigate critical exponents for blow-up of nonnegative solutions to a class of parabolic inequalities. The proofs make use of a priori estimates of solutions combined with a simple scaling argument.
On the Cauchy problem for a class of parabolic equations with variable density
The well-posedness of the Cauchy problem for a class of parabolic equations with variable density is investigated. Necessary and sufficient conditions for existence and uniqueness in the class of bounded solutions are proved. If these conditions fail, sufficient conditions are given to ensure well-posedness in the class of bounded solutions which satisfy suitable constraints at infinity.
Front propagation for nonlinear diffusion equations on the hyperbolic space
We study the Cauchy problem in the hyperbolic space for the semilinear heat equation with forcing term, which is either of KPP type or of Allen-Cahn type. Propagation and extinction of solutions, asymptotical speed of propagation and asymptotical symmetry of solutions are addressed. With respect to the corresponding problem in the Euclidean space new phenomena arise, which depend on the properties of the diffusion process in . We also investigate a family of travelling wave solutions, named...
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