On a nonlinear diffusion system arising in reactor dynamics

In this paper the existence, uniqueness and asymptotic behavior of the solutions of a nonlinear diffusion system $\text{?u}\text{?t}\text{? Lu = f(t, x, u) + (H(u))(t, x)}$, occurring in reactor dynamics is studied. The problem is approached on the bases of the monotone method and the notion of upper and lower solutions.     

Special solutions for an equation arising in sand ripple dynamics

We study a nonlinear fourth order evolution equation arising in the context of sand ripple dynamics. We analyse the set of stationary solutions and travelling waves in order to recover the observed phenomenology such as different wavelengths ripples, travelling waves, coarsening and time scales. Moreover, we construct an approximate solution which describes the early stages of the dynamics and which suggests the existence of coarsening and of time scales with different dynamical behaviour.     

Bifurcation and stability results for an equation arising in population genetics

Summary We consider a semilinear elliptic boundary value problem, which arises in population genetics. Although there is no obvious corresponding linearized problem, we establish, by using Implicit Function Theorem methods, necessary and sufficient conditions forbifurcation to occur from a branch of trivial solutions. The stability of the bifurcating solutions is also investigated.     

On the spectrum of an integro-differential equation arising in viscoelasticity theory

We study the spectral properties of a boundary value problem for an integro-differential equation arising in viscoelasticity theory. We prove that the spectrum of the boundary value problem is either completely real or contains, together with the real part, only finitely many complex eigenvalues. Bibliography: 8 titles.     

On the numerical solution of an integro-differential equation arising from wave-power hydraulics

A convergence analysis is presented for an implicit linear multistep method for solving integro-differential equations associated with multivalued maximal monotone mappings with special reference to an equation describing the wave induced motion of a body damped by Coulomb friction.     

On an eigenvalue problem arising in the study of the stability of ocean currents

We study a singular Sturm-Liouville eigenvalue problem which arises in studying the stability of rotating shallow-water shear flows on an equatorial -plane. Earlier studies have shown that the problem has only stable eigenvalues if a certain parameter exceeds 3/4. On the other hand, numerical studies have found unstable eigenvalues if is sufficiently small. In this note, we give an analytical proof that the bound of 3/4 is indeed sharp, i.e. there are instabilities for any < 3/4.     

Bifurcation of an equation arising in porous-medium combustion

We study the bifurcation of positive solutions of a steady-stateproblem arising in porous-medium combustion: We give explicit criteria for a uniquesolution for all >0 when a = 0 and for an S-shaped bifurcationcurve when a>0. We also prove a conjecture of Norbury &Stuart (1987, IMA J. Appl. Math. 39, 241–57).     

On a functional equation arising in information theory

We derive the representation of generalized additive measures of information, depending on two probability distributions and having the sum property with a regular generating function. This family of measures includes the Shannon entropy, the entropy of degree (,), the generalized information energy, the sine entropy and the generalized directed divergence.     

On a hyperbolic equation arising in electrostatic MEMS

We consider the initial–boundary value problem of a damped wave equation with singular nonlinearity, which describes an electrostatic micro-electro-mechanical system (MEMS) device. The results of the pull-in voltage λ^?${\lambda }^{?}$ being the critical threshold for global existence and quenching are obtained: if the applied voltage λ<λ^?$\lambda <{\lambda }^{?}$, then the equation admits a unique global small solution that exponentially converges to the minimal steady state, while large solution may quench in finite time; if λ>λ^?$\lambda >{\lambda }^{?}$, then any solution quenches in finite time. Finally, in the sense of the viscosity dominated limit, the asymptotic relation of solutions between the hyperbolic equation and the parabolic one is investigated. Also the related error estimates in arbitrary order are derived.     

On the Hyers-Ulam-Rassias stability of an additive functional equation in quasi-Banach spaces

In this paper we investigate the Hyers-Ulam-Rassias stability of the following functional equation:

     

A nonautonomous nonlinear functional differential equation arising in the theory of population dynamics

A nonlinear periodic functional differential equation with unbounded delay describing the growth of a single species with depensation is considered. The global bifurcation of positive periodic solutions from the null one is studied and the differences from logistic-type equations are shown, namely the multiplicity of non-trivial solutions and the occurrence of a new bifurcation phenomenon. The biological meaning of the results is discussed.     

On the qualitative behaviour of the solution to a stochastic partial functional - differential equation arising in population dynamics

Stability of the solution of a stochastic partial functional - differential equation that describes the evolution of a population is shown. A comparison between solutions of time-delayed problems and solutions of problems without time delay is given     

On the stability of an n-dimensional cubic functional equation

Let n?2 be an integer number. In this paper, we investigate the generalized Hyers-Ulam-Rassias stability in Banach spaces and also Banach modules over a Banach algebra and a C^∗-algebra, and the stability using the alternative fixed point of an n-dimensional cubic functional equation in Banach spaces: