Related papers: Free transmission problems
In this paper we study existence and uniqueness of solutions for a very general class of doubly nonlinear diffusion equations on metric graphs, which provide the appropriate mathematical framework to describe complex tubular networks in…
We study nonlinear diffusion problems of the form $u_t=u_{xx}+f(u)$ with free boundaries. Such problems may be used to describe the spreading of a biological or chemical species, with the free boundary representing the expanding front. For…
The purpose of this paper is to extend some spectral properties of regular Sturm-Liouville problems to the special type discontinuous boundary-value problem, which consists of a Sturm-Liouville equation together with…
To understand the spreading and interaction of prey and predator, in this paper we study the dynamics of the diffusive Lotka-Volterra type prey-predator model with different free boundaries. These two free boundaries, which may intersect…
We investigate systems of degenerate parabolic equations idealizing reactive solute transport in porous media. Taking advantage of the inherent structure of the system that allows to deduce a scalar Generalized Porous Medium Equation for…
A free boundary diffusive logistic model finds application in many different fields from biological invasion to wildfire propagation. However, many of these processes show a random nature and contain uncertainties in the parameters. In this…
We prove locally in time the existence of the unique smooth solution (including smooth interface) to the multidimensional free boundary problem for the thin film equation in the case of partial wetting. We also obtain the Schauder estimates…
We consider one-dimensional parabolic free boundary value problem with a nonlocal (integro-differential) condition on the free boundary. Results on $C^m$-regularity of the free boundary are obtained. In particular, a necessary and…
We obtain distribution-free bounds for various fundamental quantities used in probability theory by solving optimization problems that search for extreme distributions among all distributions with the same mean and dispersion. These…
We study the free boundary problem for a plasma-vacuum interface in ideal incompressible magnetohydrodynamics. Unlike the classical statement when the vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics, to better…
The current paper is devoted to the investigation of wave propagation phenomenon in reaction-diffusion equations with ignition type nonlinearity in time heterogeneous and random media. It is proven that such equations in time heterogeneous…
We compute the limit distribution of partial transposes (when both the number and the size of blocks tends to infinity) for a large class of ensembles of unitarily invariant random matrices. Furthermore, it is shown the asymptotic freeness…
The two-dimensional free-boundary problem describing steady gravity waves with vorticity on water of finite depth is considered. Bounds for stream functions as well as free-surface profiles and the total head are obtained under the…
We solve the linear advection-diffusion equation with a variable speed on a semi-infinite line. The variable speed is determined by an additional condition at the boundary, which models the dynamics of a contact line of a hydrodynamic flow…
We study the problem of synthesising a two-user broadcast channel using a common message, where each output terminal shares an independent source of randomness with the input terminal. This generalises two problems studied in the literature…
Free boundary problems deal with systems of partial differential equations, where the domain boundaries are apriori unknown. Due to this special characteristic, it is challenging to solve free boundary problems either theoretically or…
The purpose of this paper is three-fold. Firstly we attack a nonlinear interface problem on an unbounded domain with nonmonotone set-valued transmission conditions. The investigated problem involves a nonlinear monotone partial differential…
Some approach to the solution of boundary value problems for finding functions, which are analytical in a wedge, is proposed. If the ratio of the angle at the wedge vertex to a number \pi is rational, then the boundary value problem is…
In this study by applying an own technique we investigate some asymptotic approximation properties of new type discontinuous boundary-value problems, which consists of a Sturm-Liouville equation together with eigenparameter-dependent…
We point out that double distributions need not vanish at their boundary. Boundary terms do not change the ambiguity inherent in defining double distributions; instead, boundary conditions must be satisfied in order to switch between…