For the free boundary dynamics of the two-phase Hele-Shaw and Muskat problems, and also for the irrotational incompressible Euler equation, we prove existence locally in time when the Rayleigh-Taylor condition is initially satisfied for a 2D interface. The result for water waves was first obtained by Wu in a slightly different scenario (vanishing at infinity), but our approach is different beca...

in this paper, a boussinesq equation is solved by using the adomian's decomposition method, modified adomian's decomposition method and homotopy analysis method. the approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. the existence and uniqueness of the solution and the convergence of the propose...

a gel composite (based on polyacrylamide and crosslinker cr(iii) acetate) was prepared by solvent method (distillate and water formation) and nanoclay particle (kaolinite). using xrd tests, d001 was evaluated for kaolinite nanoparticles in gel composite. kaolinite modification using dimethyl-sulfoxide led to increase interlamellar spacing from 7.21 to 10.82 o a. based on the results obtained fo...

Often in oil reservoirs a layer of water lies under the layer of oil. The suction pressure due to a distribution of oil wells will cause the oil-water interface to rise up towards the wells. Given a particular distribution of oil wells, we are interested in finding the flow rates of each well that maximise the total flow rate without the interface breaking through to the wells. A method for fin...

Abstract. Existence of nonnegative weak solutions is shown for a thin film approximation of the Muskat problem with gravity and capillary forces taken into account. The model describes the space-time evolution of the heights of the two fluid layers and is a fully coupled system of two fourth order degenerate parabolic equations. The existence proof relies on the fact that this system can be vie...

We show the existence of self-similar solutions for Muskat equation. These are parameterized by 0<|s|≪1; they exact corners slope s at t=0 and become smooth in x t>0.

isoniazid (inh) was studied with regard to its electrochemical treatment on a strongly alkaline solution of a poly (3,4-ethylenedioxythiophene)-modified gold electrode, using both cyclic voltammetry and controlled potential techniques. this composite electrode exhibited 4-fold higher oxidation of inh, in accordance with peak densities, than the bare gold electrode. it was used the central compo...

recently, gasimov and yenilmez proposed an approach for solving two kinds of fuzzy linear programming (flp) problems. through the approach, each flp problem is first defuzzified into an equivalent crisp problem which is non-linear and even non-convex. then, the crisp problem is solved by the use of the modified subgradient method. in this paper we will have another look at the earlier defuzzifi...