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We consider a body immersed in a perfect gas and moving under the action of a constant force.
Body and gas are in thermal equilibrium. We assume a stochastic interaction body/medium: when a particle of the medium hits the body,
it is absorbed and immediately re-emitted with a Maxwellian distribution. This system gives rise to a microscopic model of friction.
We study the approach of the body velocity V(t) to the limiting velocity and prove that, under suitable smallness
assumptions, the approach...
We consider the problem of motion of several rigid bodies in a viscous fluid. Both compressible and incompressible fluids are studied. In both cases, the existence of globally defined weak solutions is established regardless possible collisions of two or more rigid objects.
Some general multiplicity results for critical points of parameterized functionals on reflexive Banach spaces are established. In particular, one of them improves some aspects of a recent result by B. Ricceri. Applications to boundary value problems are also given.
Recent papers have studied the existence of phase transition solutions for Allen–Cahn type equations. These solutions are either single or multi-transition spatial heteroclinics or homoclinics between simpler equilibrium states. A sufficient condition for the construction of the multitransition
solutions is that there are gaps in the ordered set of single transition solutions. In this paper we explore the necessity of these gap conditions.
We study a class of logarithmic fractional Schrödinger equations with possibly vanishing potentials. By using the fibrering maps and the Nehari manifold we obtain the existence of at least one nontrivial solution.
We consider the Neumann problem for an elliptic system of two equations involving the critical Sobolev nonlinearity. Our main objective is to study the effect of the coefficient of the critical Sobolev nonlinearity on the existence and nonexistence of least energy solutions. As a by-product we obtain a new weighted Sobolev inequality.
We establish the existence of solutions for the Neumann problem for a system of two equations involving a homogeneous nonlinearity of a critical degree. The existence of a solution is obtained by a constrained minimization with the aid of P.-L. Lions' concentration-compactness principle.
We establish the existence of multiple solutions of an asymptotically linear Neumann problem. These solutions are obtained via the mountain-pass principle and a local minimization.
We investigate the solvability of the linear Neumann problem (1.1) with L¹ data. The results are applied to obtain existence theorems for a semilinear Neumann problem.
We study the flat region of stationary points of the functional under the constraint , where is a bounded domain in . Here is a function which is concave for small and convex for large, and is a given constant. The problem generalizes
the classical minimal resistance body problems considered by Newton. We construct a family of partially flat radial solutions to the associated stationary problem when is a ball. We also analyze some other qualitative properties. Moreover, we show the...
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