We consider a coupled PDE system arising in noise reduction problems. In a two dimensional chamber, the acoustic pressure (unwanted noise) is represented by a hyperbolic wave equation. The floor of the chamber is subject to the action of piezo-ceramic patches (smart materials). The goal is to reduce the acoustic pressure by means of the vibrations of the floor which is modelled by a hyperbolic ...

sorption reactions in many heterogeneous systems are important. adsorption is a time dependent process and knowing the adsorption rate is essential for designing, evaluating and recovering the adsorbents. at the present study, an ammonium adsorption kinetic experiment by some soils series of golestan provice, which is varying in mineralogical and textural properties was conducted using solution...

This paper considers the optimal control of a degenerate parabolic partial differential equation governing a di usive population with logistic growth terms. Assuming this population causes damage to forest and agricultural land, the optimal control is the trapping rate and the cost functional is a combination of the damage and trapping costs. We prove existence, uniqueness, and regularity resul...

This is the second paper of a series in which we analyze mathematical properties and develop numerical methods for a degenerate elliptic-parabolic partial diierential system which describes the ow of two incom-pressible, immiscible uids in porous media. In this paper we consider a nite element approximation for this system. The elliptic equation for the pressure and velocity is approximated by ...

We are interested in the large-time behavior of periodic entropy solutions in L to anisotropic degenerate parabolic-hyperbolic equations of second-order. Unlike the pure hyperbolic case, the nonlinear equation is no longer self-similar invariant and the diffusion term in the equation significantly affects the large-time behavior of solutions; thus the approach developed earlier based on the sel...

Methods are developed for extracting from a numerical propagating-beam solution of a scalar wave equation the information necessary to compute the impulse-response function and the pulse dispersion for a multimode graded-index fiber. It is shown that the scalar Helmholtz equation and the parabolic wave equation have the same set of eigenfunctions in common and that the eigenvalues for the two e...

§0 Introduction. In a recent paper of Perelman[P1], an entropy formula for Ricci flow was derived. The formula turns out being of fundamental importance in the study of Ricci flow (cf. [P1, Sections 3, 4, 10]) as well as the Kähler-Ricci flow [P2]. The derivation of the entropy formula in [P1, Section 9] resembles the gradient estimate for the linear heat equation proved by Li-Yau in another fu...

Sufficient conditions are obtained so that a weak subsolution of (0.1), bounded from above on the parabolic boundary of the cylinder Q, turns out to be bounded from above in Q.

A boundary value problem for a fractional power of the second-order elliptic operator is considered. It is solved numerically using a time-dependent problem for a pseudo-parabolic equation. For the auxiliary Cauchy problem, the standard two-level schemes with weights are applied. Stability conditions are obtained for the fully discrete schemes under the consideration. The numerical results are ...

Convergence of Rothe’s method for the fully nonlinear parabolic equation ut +F (D 2u,Du, u, x, t) = 0 is considered under some continuity assumptions on F. We show that the Rothe solutions are Lipschitz in time, and they solve the equation in the viscosity sense. As an immediate corollary we get Lipschitz behavior in time of the viscosity solutions of our equation.