Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations
Some compactness methods in the theory of nonlinear evolution equations with applications to P.D.E.
Some (new) counterexamples of parabolic systems
We give examples of parabolic systems (in space dimension ) having a solution with real analytic initial and boundary values which develops the discontinuity in the interior of the parabolic cylinder.
Some new results on a Stefan problem in a concentrated capacity
An existence and uniqueness theorem for a nonlinear parabolic system of partial differential equations, connected with the theory of heat conduction with a transition phase in a concentrated capacity, is given in sufficiently general hypotheses on the data.
Some nonexistence results for higher-order evolution inequalities in cone-like domains.
Some problems for nonlinear pseudoparabolic equations in nontube domains.
Some properties of solutions for the generalized thin film equation in one space dimension.
Some regularity results for quasi-linear parabolic systems
Some regularity results for quasilinear parabolic systems
Some remarks on the Galerkin approximation of parabolic equations
Some simple nonlinear PDE's without solutions
In questo articolo consideriamo alcune semplici equazioni a derivate parziali elittiche nonlineari, per le quali il Teorema della Funzione Inversa, se applicato in modo formale, suggerisce l'esistenza di soluzioni. Nonostante ciò, proviamo che non esistono soluzioni neppure in vari sensi deboli. Un problema modello è dato da in , su , dove , , è un dominio limitato contenente . Per qualunque costante , arbitrariamente piccola, proviamo che questo problema non ammette soluzioni distribuzionali...
Some theorems on partial differential inequalities of parabolic type
Source type positive solutions of nonlinear parabolic inequalities
Space dimension can prevent the blow-up of solutions for parabolic problems.
Spectrum of the linearized operator for the Ginzburg-Landau equation.
Spreading and vanishing in nonlinear diffusion problems with free boundaries
We study nonlinear diffusion problems of the form with free boundaries. Such problems may be used to describe the spreading of a biological or chemical species, with the free boundary representing the expanding front. For special of the Fisher-KPP type, the problem was investigated by Du and Lin [DL]. Here we consider much more general nonlinear terms. For any which is and satisfies , we show that the omega limit set of every bounded positive solution is determined by a stationary solution....
Stability analysis of a model of atherogenesis: an energy estimate approach. II.
Stability and consistency of the semi-implicit co-volume scheme for regularized mean curvature flow equation in level set formulation
We show stability and consistency of the linear semi-implicit complementary volume numerical scheme for solving the regularized, in the sense of Evans and Spruck, mean curvature flow equation in the level set formulation. The numerical method is based on the finite volume methodology using the so-called complementary volumes to a finite element triangulation. The scheme gives the solution in an efficient and unconditionally stable way.
Stability and continuous dependence of solutions of one-phase Stefan problems for semilinear parabolic equations.
Stability for a diffusive delayed predator-prey model with modified Leslie-Gower and Holling-type II schemes
A diffusive delayed predator-prey model with modified Leslie-Gower and Holling-type II schemes is considered. Local stability for each constant steady state is studied by analyzing the eigenvalues. Some simple and easily verifiable sufficient conditions for global stability are obtained by virtue of the stability of the related FDE and some monotonous iterative sequences. Numerical simulations and reasonable biological explanations are carried out to illustrate the main results and the justification...