in this paper, we study the nehari manifold and its application on the following navier boundary valueproblem involving the p-biharmonic          0, on( ) 1 ( , ) , in , 2*2u uf x u u upu u p q where  is a bounded domain in rn with smooth boundary  . we prove that the problem has atleast two nontrivial nonnegtive solutions when the parameter  belongs to a certain subset o...

We investigate the Dirichlet problem for the parabolic equation ut=Δum−buβ, m > 0, β > 0, b ∈ R, in a nonsmooth and closed domain Ω ⊂ RN+1, N ≥ 2, possibly formed with irregular surfaces and having a characteristic vertex point. Existence, boundary regularity, uniqueness, and comparison results are established. The main objective of the paper is to express the criteria for the well-posedness in...

For all N ≥ 9, we find smooth entire epigraphs in R , namely smooth domains of the form Ω := {x ∈ R / xN > F (x1, . . . , xN−1)}, which are not half-spaces and in which a problem of the form ∆u+ f(u) = 0 in Ω has a positive, bounded solution with 0 Dirichlet boundary data and constant Neumann boundary data on ∂Ω. This answers negatively for large dimensions a question by Berestycki, Caffarelli ...

We discuss the coupling processes between surface gravity waves and adjacent winds and currents in turbulent boundary layers. These processes mediate exchanges of momentum, heat, and gases between the atmosphere and ocean and thus are of global significance for climate. Surface waves grow primarily by pressure-form stress from airflow over the waveforms, and they dissipate in the open sea by wa...

This paper is concerned with the motion of electrically charged particles in \curved" inn-nite strip. The equations of motion are ' = with initial and boundary conditions, where ' is the electric potential, is the particle trajectory, P is the charge distribution, and J is the Jacobian. The lower boundary ? 0 of the strip is grounded. Therefore, once a particle reaches ? 0 ; it loses its charge...

For a simple graph G = (V,E), the vertex boundary of a subset A ⊆ V consists of all vertices not in A that are adjacent to some vertex in A. The goal of the vertex isoperimetric problem is to determine the minimum boundary size of all vertex subsets of a given size. In particular, define μG(r) as the minimum boundary size of all vertex subsets of G of size r. Meanwhile, the vertex set of the Kn...

We present the theory of the multi-α-solutions of the variational problem for the upper bounds on the convective heat transport in a heated from below horizontal fluid layer with rigid lower boundary and stress-free upper boundary. A sequence of upper bounds on the convective heat transport is obtained. The highest bound Nu = 1+(1/6)R is between the bounds Nu = 1+0.152R for the case of a fluid ...

in this paper, the accuracy of k- and k- turbulence models in super sonic boundary layer capturing of smooth/rough flat plates have been comprehensively investigated. among these investigations, some sorts of sensitivity analysis, including change in turbulence model, generated-grid density, near wall affects, c magnitude (for boundary layers generated on smooth flat plates), and change in c...