We consider the Dirichlet-to-Neumann operator in strip-like and half-space domains with Lipschitz boundary. It is shown that quadratic form generated by controls some sharp homogeneous fractional Sobolev norms. As an application, we prove global solutions constructed Dong et al. (2021) for one-phase Muskat problem decays exponentially time any Hölder norm Cα, α ∈ (0,1).

Abstract We construct mixing solutions to the incompressible porous media equation starting from Muskat type data in partially unstable regime. In particular, we consider bubble and turned interfaces with Sobolev regularity. As a by-product, prove continuation of evolution IPM after Rayleigh–Taylor smoothness breakdown exhibited (Castro et al. Arch Ration Mech Anal 208(3):805–909, 2013, Castro ...

in this work, a new, simple and fast method for the solid phase extraction-spectrophotometric determination of phosphate using cetyltrimethyl ammonium bromide immobilized on alumina-coated magnetite nanoparticles (ctab@acmnps) has been developed. the determination of phosphate is based on the molybdenum blue method which was monitored at λmax of 810 nm. mnps and acmnps characterized by sem, vsm...

this paper presents a comparison between variational iteration method (vim) and modfied variational iteration method (mvim) for approximate solution a system of volterra integral equation of the first kind. we convert a system of volterra integral equations to a system of volterra integro-di®erential equations that use vim and mvim to approximate solution of this system and hence obtain an appr...

We consider the problem of the evolution of the interface given by two incompressible fluids through a porous medium, which is known as the Muskat problem and in two dimensions it is mathematically analogous to the two-phase Hele-Shaw cell. We focus on a fluid interface given by a jump of densities, being the equation of the evolution obtained using Darcy’s law. We prove local well-posedness wh...