Abstract. A fully coupled system of two second-order parabolic degenerate equations arising as a thin film approximation to the Muskat problem is interpreted as a gradient flow for the 2-Wasserstein distance in the space of probability measures with finite second moment. A variational scheme is then set up and is the starting point of the construction of weak solutions. The availability of two ...

In this work we study the inhomogeneous Muskat problem, \emph{i.e.} evolution of an internal wave between two different fluids in a porous medium with discontinuous permeability. particular, under precise conditions on initial datum and physical quantities our results ensure decay solutions towards equilibrium state Lipschitz norm. addition, establish global existence solutions.

The singular limit of the thin film Muskat problem is performed when density (and possibly viscosity) lighter fluid vanishes and porous medium equation identified as problem. In particular, height denser shown to converge towards solution an explicit rate for this convergence provided in space dimension d ⩽ 4. Moreover, determined a certain regime given by corresponding initial condition.

in this study, undoped zno and doped with fe and mn nanostructures were synthesized by hydrothermal method. the morphology of nanostructures was characterized by scanning electron microscope. the electrochemical response of the carbon paste electrode modified with nanoparticles of zno and also zno doped with fe and mn toward levodopa (l-dopa) was studied. studies of cyclic voltammetry using pro...

This paper is devoted to the study of solutions with critical regularity for two-dimensional Muskat equation. We prove that Cauchy problem well-posed on endpoint Sobolev space $$L^2$$ functions three-half derivative in . result optimal respect scaling One well-known difficulty one cannot define a flow map such lifespan bounded from below subsets this space. To overcome this, we estimate norm wh...

we are concerned with the development of a k−step method for the numerical solution of fuzzy initial value problems. convergence and stability of the method are also proved in detail. moreover, a specific method of order 4 is found. the numerical results show that the proposed fourth order method is efficient for solving fuzzy differential equations.

the charge transfer (ct) complex formation of benzonitrile as acceptor with the aromatic donors o-, m-, p-xylene and ethylbenzene in ccl4 solutions is investigated by chemical shift measurements relative to an external reference. the equilibrium parameters, q and dad of their weak molecular complexes, as found numerically modified cresswel- allred (c-a) method, is compared with graphically scat...

the burgers’ equation is a simplified form of the navier-stokes equations that very well represents their non-linear features. in this paper, numerical methods of the adomian decomposition and the modified crank – nicholson, used for solving the one-dimensional burgers’ equation, have been compared. these numerical methods have also been compared with the analytical method. in contrast to...