In this paper we study the initial boundary value problem for system ut??um=?div(uq?v),vt??v+v=u. This is so-called Keller-Segel model with nonlinear diffusion. Our investigation reveals that diffusion can prevent overcrowding. To be precise, show solutions are bounded as long m>q>0, thereby substantially generalizing known results in area. Furthermore, our result seems to imply have and blow-u...

Hydrogen diffusion on metals exhibits rich quantum behavior, which is not yet fully understood. Using simulations, we show that many hydrogen diffusion barriers can be categorized into those with parabolic tops and those with broad tops. With parabolic-top barriers, hydrogen diffusion evolves gradually from classical hopping, to shallow tunneling, to deep tunneling as the temperature (T) decrea...

In the FIDA experiment, a pressure gradient generates the flow resulting in a parabolic flow profile. The parabolic flow profile inside the capillary distorts the indicator zone resulting in a concentration gradient between the center and the periphery of the capillary (figure S1). Equation 5 in the main manuscript is valid provided there is sufficient time for radial diffusion, and that advect...

This paper studies the global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with appropriate initial and mixed boundary conditions. Under some practicable regularity criteria on diffusion item and nonlinearity, we establish the local existence and uniqueness of classical solutions based on a contraction mapping. This local solution can be conti...

This work aims to investigate the competitive time-dependent desorption rate of heavy metals (lead, zinc, nickel) coexisting with phenanthrene from natural high buffering soil. Two non-ionic surfactants (Tween 80 and Brij 35) combined with disodium ethylene diamine tetraacetate salt (Na2-EDTA) were utilized as the reagents. The contaminants’ time-dependent desorption data was fitted with five k...

In a series of papers [1]–[4] we considered parabolic equations for measures on R. Our motivation was a study of the Kolmogorov equations for transition probabilities of diffusion processes. Here we are concerned with similar problems in infinite dimensions. Applications are given to stochastic partial differential equations such as stochastic equations of Navier– Stokes and reaction-diffusion ...

We study the inverse problem of the simultaneous identification of two discontinuous diffusion coefficients for a one-dimensional coupled parabolic system with the observation of only one component. The stability result for the diffusion coefficients is obtained by a Carleman-type estimate. Results from numerical experiments in the one-dimensional case are reported, suggesting that the method m...

The global-in-time existence of nonnegative solutions to a parabolic strongly coupled system with mixed Dirichlet-Neumann boundary conditions is shown. The system describes the time evolution of the electron and hole densities in a semiconductor when electron-hole scattering is taken into account. The parabolic equations are coupled to the Poisson equation for the electrostatic potential. Writt...

Conditional Lie symmetries of semi-linear 1D Schrödinger and diffusion equations are studied if the mass (or the diffusion constant) is considered as an additional variable. In this way, dynamical symmetries of semi-linear Schrödinger equations become related to the parabolic and almostparabolic subalgebras of a three-dimensional conformal Lie algebra (conf3)C. We consider nonhermitian represen...