We analyse the effect of the mechanical response of the solid phase during liquid/solid phase change by numerical simulation of a benchmark test based on the well-known and debated experiment of melting of a pure gallium slab counducted by Gau & Viskanta in 1986. The adopted mathematical model includes the description of the melt flow and of the solid phase deformations. Surprisingly the conclusion reached is that, even in this case of pure material, the contribution of the solid phase to the...

We demonstrate a theorem of existence and uniqueness on a large scale of the solution of a system of differential disequations associated to a Graffi model relative to the motion of two incompressible viscous fluids.

In this paper, we propose a computational model to investigate the coupling between cell’s adhesions and actin fibres and how this coupling affects cell shape and stability. To accomplish that, we take into account the successive stages of adhesion maturation from adhesion precursors to focal complexes and ultimately to focal adhesions, as well as the actin fibres evolution from growing filaments, to bundles and finally contractile stress fibres.We use substrates with discrete patterns of adhesive...

We consider higher order mixed finite element methods for the incompressible Stokes or Navier-Stokes equations with Qr-elements for the velocity and discontinuous $P_{r-1}$-elements for the pressure where the order r can vary from element to element between 2 and a fixed bound $r^{*}$. We prove the inf-sup condition uniformly with respect to the meshwidth h on general quadrilateral and hexahedral meshes with hanging nodes.

By deriving a variant of interpolation inequality, we obtain a sharp criterion for global existence and blow-up of solutions to the inhomogeneous nonlinear Schrödinger equation with harmonic potential $$\mathrm{i}{\varphi }_t=-▵\varphi +{\left|x\right|}^2\varphi -{\left|x\right|}^b{\left|\varphi \right|}^{p-2}\varphi .$$ We also prove the existence of unstable standing-wave solutions via blow-up under certain conditions on the unbounded inhomogeneity and the power of nonlinearity, as well as the frequency of the wave.

For an equation of the type of porous media equation the Cauchy-Dirichlet and Cauchy-Neumann problems are considered. The existence and uniqueness results in the case of $L^{\infty }$ initial and boundary data are given.

We consider the spatial behavior of the velocity field $u(x,t)$ of a fluid filling the whole space ${ℝ}^n$ ($n\ge 2$) for arbitrarily small values of the time variable. We improve previous results on the spatial spreading by deducing the necessary conditions $\int u_h(x,t)u_k(x,t)\mathrm{d}x=c\left(t\right){\delta }_{h,k}$ under more general assumptions on the localization of $u$. We also give some new examples of solutions which have a stronger spatial localization than in the generic case.

We consider the spatial behavior of the velocity field u(x, t) of a fluid filling the whole space ${}^n$ ($n\ge 2$) for arbitrarily small values of the time variable. We improve previous results on the spatial spreading by deducing the necessary conditions $\int u_h(x,t)u_k(x,t)\mathrm{d}x=c\left(t\right){\delta }_{h,k}$ under more general assumptions on the localization of u. We also give some new examples of solutions which have a stronger spatial localization than in the generic case.

We consider a nonnegative superbiharmonic function $w$ satisfying some growth condition near the boundary of the unit disk in the complex plane. We shall find an integral representation formula for $w$ in terms of the biharmonic Green function and a multiple of the Poisson kernel. This generalizes a Riesz-type formula already found by the author for superbihamonic functions $w$ satisfying the condition $0\le w\left(z\right)\le C(1-|z\left|\right)$ in the unit disk. As an application we shall see that the polynomials are dense in weighted Bergman...

The Povzner equation is a version of the nonlinear Boltzmann equation, in which the collision operator is mollified in the space variable. The existence of stationary solutions in $L^1$ is established for a class of stationary boundary-value problems in bounded domains with smooth boundaries, without convexity assumptions. The results are obtained for a general type of collision kernels with angular cutoff. Boundary conditions of the diffuse reflection type, as well as the given incoming profile, are...