Continuous dependence and stability for non linear dispersive and dissipative waves
Sui campi magnetici possibili in un fluido conduttore uniformemente ruotante.
Asymptotic Behaviour of Solutions to a Nonlinear Third Order P.D.E. Modeling Physical Phenomena
The longtime behaviour of the solutions to the initial boundary value problem (1.1)-(1.3) modeling various physical phenomena, either in the autonomous case or in the nonautonomous case, is studied. Conditions guaranteeing ultimately boundedness and conditions guaranteeing nonlinear asymptotic global stability of the null solution are obtained. Boundary conditions, different from (1.2)1-(1.2)2, are also considered (Section 9).
A Peculiar Liapunov Functional for Ternary Reaction-Diffusion Dynamical Systems
A Liapunov functional , depending - together with the temporal derivative along the solutions - on the eigenvalues via the system coefficients, is found. This functional is ``peculiar'' in the sense that is positive definite and simultaneously is negative definite, if and only if all the eigenvalues have negative real part. An application to a general type of ternary system often encountered in the literature, is furnished.
-stability of the solutions to a nonlinear binary reaction-diffusion system of P.D.E.s
The -stability (instability) of a binary nonlinear reaction diffusion system of P.D.E.s - either under Dirichlet or Neumann boundary data - is considered. Conditions allowing the reduction to a stability (instability) problem for a linear binary system of O.D.E.s are furnished. A peculiar Liapunov functional linked (together with the time derivative along the solutions) by direct simple relations to the eigenvalues, is used.
Unconditional nonlinear exponential stability in the Bénard problem for a mixture: necessary and sufficient conditions
The Lyapunov direct method is applied to study nonlinear exponential stability of a basic motionless state to imposed linear temperature and concentration fields of a binary fluid mixture heated and salted from below, in the Oberbeck-Boussinesq scheme. Stress-free and rigid surfaces are considered and absence of Hopf bifurcation is assumed. We prove the coincidence of the linear and (unconditional) nonlinear critical stability limits, when the ratio between the Schmidt and the Prandtl numbers is...
Unconditional nonlinear stability in a polarized dielectric liquid
We derive a very sharp nonlinear stability result for the problem of thermal convection in a layer of dielectric fluid subject to an alternating current (AC). It is particularly important to note that the size of the initial energy in which we establish global nonlinear stability is not restricted whatsoever, and the Rayleigh-Roberts number boundary coincides with that found by a formal linear instability analysis.
On the temperature distribution in cold ice
The linear heat equation predicts that the variations of temperature along a cold ice sheet {i.e. at a temperature less than is freezing point) due to a sudden increase in air temperature, are very very slow. Based on this we represent the nonlinear evolution of an ice sheet as a sequence of steady states. As a first fundamental indication that this model is correct well posedness with respect to the variations of initial and boundary data is proved. Further an estimate of the error made in evaluating...
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