On the uniqueness of the second bound state solution of a semilinear equation
On the uniqueness of viscosity solutions for first order partial differential-functional equations
We consider viscosity solutions for first order differential-functional equations. Uniqueness theorems for initial, mixed, and boundary value problems are presented. Our theorems include some results for generalized ("almost everywhere") solutions.
On the validity of Friedrichs' inequalities.
On the validity of Huygens' principle for second order partial differential equations with four independent variables. II. A sixth necessary condition
On the validity of Huygens' principle for second order partial differential equations with four independent variables. Part I : derivation of necessary conditions
On the viscous Allen-Cahn and Cahn-Hilliard systems with Willmore regularization
We consider the viscous Allen-Cahn and Cahn-Hilliard models with an additional term called the nonlinear Willmore regularization. First, we are interested in the well-posedness of these two models. Furthermore, we prove that both models possess a global attractor. In addition, as far as the viscous Allen-Cahn equation is concerned, we construct a robust family of exponential attractors, i.e. attractors which are continuous with respect to the perturbation parameter. Finally, we give some numerical...
On the viscous Burgers equation in unbounded domain.
On the -regularity of solutions to systems of differential equations in the case when the equations are constructed from discontinuous functions.
On the wave equations in the spacetime of a cosmic string
On the wave equations with memory in noncylindrical domains.
On the weak solution of a three-point boundary value problem for a class of parabolic equations with energy specification.
On the Weak Solutions of the McKendrick Equation: Existence of Demography Cycles
We develop the qualitative theory of the solutions of the McKendrick partial differential equation of population dynamics. We calculate explicitly the weak solutions of the McKendrick equation and of the Lotka renewal integral equation with time and age dependent birth rate. Mortality modulus is considered age dependent. We show the existence of demography cycles. For a population with only one reproductive age class, independently of the stability of the weak solutions and after a transient time,...
On the weakly nonlinear wave equation involving a small parameter at the highest derivative
On the well-posedness of some optimal control problems
Si considerano problemi di controllo ottimale con una dipendenza non lineare tra il controllo e lo stato. Si mostra come in certi casi la continuità di tale dipendenza, quindi la buona posizione nel senso di Tychonov, è connessa alla forma del funzionale costo. In particolare si esamina un problema di Stefan a due fasi con controllo distribuito nel termine di sorgente.
On the asymptotic properties of solutions of the Navier-Stokes equations in the half-space.
On the Yang-Mills heat equation in two and three dimensions.
On the -convergence of Laplace-Beltrami operators in the plane.
On three-dimensional vortex patches
On three-point boundary value problem with a weighted integral condition for a class of singular parabolic equations.
On Two-Dimensional Elliptic Systems with a One-sided Condition.