Related papers: Counterexamples to quasiconcavity for the heat equ…
In this paper, we consider the heat flow for p-pseudoharmonic maps from a closed Sasakian manifold M into a compact Riemannian manifold N. We prove global existence and asymptotic convergence of the solution for the p-pseudoharmonic map…
In this paper we construct explicit examples that show the sublevel sets of the solution of a $k$-Hessian equation defined on a convex ring do not have to be convex.
The understanding of the underlying dynamical mechanisms which determine the macroscopic laws of heat conduction is a long standing task of non-equilibrium statistical mechanics. A better understanding of the mechanism of heat conduction…
The aim of this work is twofold. From a mathematical point of view, we show the existence of a hyperbolic system of equations that is not symmetrizable in the sense of Friedrichs. Such system appears in the theory of compressible fluid…
We build up a decomposition for the flow generated by the heat equation with a real analytic memory kernel. It consists of three components: The first one is of parabolic nature; the second one gathers the hyperbolic component of the…
We demonstrate the existence of quasiconformal mappings on closed manifolds that cannot be decomposed as a composition of mappings with arbitrarily small conformal distortion.
In this paper we obtain necessary conditions on the initial value for the solvability of the Cauchy problem for semilinear heat equations. These necessary conditions were already obtained in the framework of integral solutions, but not in…
An initial-boundary value problem for the time-fractional diffusion equation is discretized in space using continuous piecewise-linear finite elements on a polygonal domain with a re-entrant corner. Known error bounds for the case of a…
I use a simple analytical model to show that simple heat conduction models cannot significantly suppress cluster cooling flows. I build a static medium where heat conduction globally balances radiative cooling, and then perturb it. I show…
We establish global existence of smooth solutions to heat flow for Yang-Mills-Higgs functional on Kahler fibrations. As an application, we give a new proof of the key inequality for Mundet's Hitchin-Kobayashi correspondence theorem using…
We study the linear heat equation on a halfspace with a linear dynamical boundary condition. We are interested in an appropriate choice of the function space of initial functions such that the problem possesses a solution. It was known…
In this paper, we first establish regularity of the heat flow of biharmonic maps into the unit sphere $S^L\subset\mathbb R^{L+1}$ under a smallness condition of renormalized total energy. For the class of such solutions to the heat flow of…
Numerical simulations of quasi-static magnetoconvection with a vertical magnetic field are carried out up to a Chandrasekhar number of $Q=10^8$ over a broad range of Rayleigh numbers $Ra$. Three magnetoconvection regimes are identified: two…
A map from the initial conditions to the values of the function and its first spatial derivative evaluated at the interface is constructed for the heat equation on finite and infinite domains with $n$ interfaces. The existence of this map…
Due to ample applications from medical services to industrial activities, the study of flow and heat transfer through a curved duct has attracted considerable attention to the researchers. In this paper, a comprehensive numerical study is…
A cold, thin film of liquid impinging on an isothermal hot, horizontal surface has been investigated. An approximate solution for the velocity and temperature distributions in the flow along the horizontal surface is developed, which…
Laboratory experiments were conducted to study heat transport characteristics in a nonhomogeneously heated fluid annulus subjected to rotation along the vertical axis (z). The nonhomogeneous heating was obtained by imposing radial and…
We show that the porous medium equation does not in general preserve $\alpha$-concavity of the pressure for $0\le\alpha<1/2$ or $1/2<\alpha\le 1$. In particular, this resolves an open problem of V\'azquez on whether concavity of pressure is…
We prove new Lipschitz properties for transport maps along heat flows, constructed by Kim and Milman. For (semi)-log-concave measures and Gaussian mixtures, our bounds have several applications: eigenvalues comparisons, dimensional…
Similarity solutions for the two-phase Rubinstein binary-alloy solidification problem in a semi-infinite material are developed. These new explicit solutions are obtained by considering two cases: a heat flux or a convective boundary…