On a boundary-value problem posed by cancer therapy with neutron beams

A Well-Posed Free Boundary Value Problem for a Hyperbolic Equation with Dirichlet Boundary Conditions

We construct solutions of a free boundary value problem for a hyperbolic equation with Dirichlet boundary data. This problem arises from a model of deformation of granular media.

Well-Posed Initial-Boundary Value Problem for Constrained Evolution

An initial - boundary - value problem for the Korteweg - deVries equation posed on a nite

R esum e. La propagation unidirectionnelle d'ondes de faible amplitude et de grande longueur d'onde est d ecrite, dans de nombreux syst emes physiques, par l' equation de Korteweg-de Vries. L'objet de ce travail est de proposer un probl eme mixte bien pos e lorsque le do-maine spatial est born e. Plus pr ecis ement nous etablissons l'existence de solutions locales en temps pour des donn ees ini...

MIXED BOUNDARY VALUE PROBLEM FOR A QUARTER-PLANE WITH A ROBIN CONDITION

We consider a mixed boundary value problem for a quarter-plane with a Robin condition on one edge. We have developed two procedures, one based on the advanced theory of dual integral equations and the other, in our opinion simpler technique, relying on conformal mapping. Both of the procedures are of interest, because the former may be easier to adapt to other boundary value problems.

On boundary value problem for fractional differential equations

In this paper‎, ‎we study the existence of solutions for a‎ ‎ fractional boundary value problem‎. ‎By using critical point theory‎ ‎ and variational methods‎, ‎we give some new criteria to guarantee‎ ‎ that‎ ‎ the problems have at least one solution and infinitely many solutions.