We prove the strong Feller property and exponential mixing for 3D stochastic Navier-Stokes equation driven by mildly degenerate noises (i.e. all but finitely many Fourier modes are forced) via Kolmogorov equation approach.

In this paper a closed form solution for one-dimensional magnetothermoelastic problem in a functionally graded material (FGM) hollow sphere placed in a uniform magnetic field and temperature field subjected to an internal pressure is obtained using the theory of magnetothermoelasticity. Hyper-geometric functions are employed to solve the governing equation. The material properties through the g...

In this survey we recall the results obtained in [16] where we gave a representation theorem for the solutions of stochastic di¤erential equations in Hilbert spaces. Using this representation theorem and the deterministic characterizations of exponential stability and uniform observability obtained in [16], [17], we will prove a result of Datko type concerning the exponential dichotomy of stoch...

In this paper, I will prove that assuming Schanuel’s conjecture, an exponential polynomial with algebraic coefficients can have only finitely many algebraic roots. Furthermore, this proof demonstrates that there are no unexpected algebraic roots of any exponential polynomial. This implies a special case of Shapiro’s conjecture: if p(x) and q(x) are two exponential polynomials over the algebraic...

We prove an eeective mean-value theorem for the values of a non-degenerate, algebraic exponential polynomial in several variables. These objects simultaneously generalise the fundamental examples of linear recurrence sequences and sums of S-units. The proof is based on an eeective, uniform estimate for the deviation of the exponential polynomial from its expected value. This estimate is also us...

Modeling the flow curves of materials at elevated temperatures is the first step in mathematical simulation of the hot deformation processes of them. In this work a comparative study was provided to examine the capability of three different constitutive equations in modeling the hot deformation flow curves of AZ91 magnesium alloy. For this, the Arrhenius equation with strain dependent constants...

A Hamiltonian system is studied which has a term approaching a constant at an exponential rate at infinity . A minimax argument is used to show that the equation has a positive homoclinic solution. The proof employs the interaction between translated solutions of the corresponding homogeneous equation. What distinguishes this result from its few predecessors is that the equation has a nonhomoge...

We study stability of linear time-varying differential-algebraic equations (DAEs). The Bohl exponent is introduced and finiteness of the Bohl exponent is characterized, the equivalence of exponential stability and a negative Bohl exponent is shown and shift properties are derived. We also show that the Bohl exponent is invariant under the set of Bohl transformations. For the class of DAEs which...

We study the Darboux integrability of the celebrated Falkner– Skan equation f ′′′+ff ′′+λ(1−f ′2) = 0, where λ is a parameter. When λ = 0 this equation is known as Blasius equation. We show that both differential systems have no first integrals of Darboux type. Additionally we compute all the Darboux polynomials and all the exponential factors of these differential equations.

The global-in-time existence of weak nonnegative solutions to a sixth-order nonlinear parabolic equation in one space dimension with periodic boundary conditions is proved. The equation arises from an approximation of the quantum drift-diffusion model for semiconductors and describes the evolution of the electron density in the semiconductor crystal. The existence result is based on two techniq...