The Muskat problem and related topics

Porous media: the Muskat problem in 3D

The Muskat problem involves filtration of two incompressible fluids throughout a porous medium. In this paper we shall discuss in 3-D the relevance of the RayleighTaylor condition, and the topology of the initial interface, in order to prove its local existence in Sobolev spaces.

Hilbert ’ s fifth problem and related topics

the evaluation of language related engagment and task related engagment with the purpose of investigating the effect of metatalk and task typology

abstract while task-based instruction is considered as the most effective way to learn a language in the related literature, it is oversimplified on various grounds. different variables may affect how students are engaged with not only the language but also with the task itself. the present study was conducted to investigate language and task related engagement on the basis of the task typolog...

On the isomorphism problem of Coxeter groups and related topics

At the conference the author gives a talk which surveys the definition, history and preceding results on the isomorphism problem of Coxeter groups (problem of deciding which Coxeter groups are isomorphic), together with backgrounds for Coxeter groups, applications of this problem and some related topics in the theory of Coxeter groups, including the author’s recent works. The author would like ...

On the global existence for the Muskat problem

The Muskat problem models the dynamics of the interface between two incompressible immiscible fluids with different constant densities. In this work we prove three results. First we prove an L(R) maximum principle, in the form of a new “log” conservation law (3) which is satisfied by the equation (1) for the interface. Our second result is a proof of global existence of Lipschitz continuous sol...