We obtain Strichartz estimates for the fractional heat equations by using both the abstract Strichartz estimates of Keel-Tao and the HardyLittlewood-Sobolev inequality. We also prove an endpoint homogeneous Strichartz estimate via replacing L∞x (R ) by BMOx(R) and a parabolic homogeneous Strichartz estimate. Meanwhile, we generalize the Strichartz estimates by replacing the Lebesgue spaces with...

In this work a new and promising algorithm based on the minimization of especial functional that depends on two regularization parameters is considered for the identification of the heat conduction coefficient in the parabolic equation. This algorithm uses the adjoint and sensibility equations. One of the regularization parameters is associated with the heat-coefficient (as in conventional Tikh...

4 Initial Value Problems for PDEs 18 4.1 Heat Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.2 FDMs for Parabolic Problems . . . . . . . . . . . . . . . . . . . . 19 4.2.1 Error Analysis . . . . . . . . . . . . . . . . . . . . . . . . 20 4.3 Mixed IVP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.3.1 Implicit Scheme . . . . . . . . . . . . . . . . . . ....

In this paper, we investigate the system of compressible Navier-Stokes equations with hyperbolic heat conduction, i.e., replacing the Fourier’s law by Cattaneo’s law. First, by using Kawashima’s condition on general hyperbolic parabolic systems, we show that for small relaxation time τ , global smooth solution exists for small initial data. Moreover, as τ goes to zero, we obtain the uniform con...

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author Mathias Masson Name of the doctoral dissertation Regularity for parabolic quasiminimizers in metric measure spaces Publisher School of Science Unit Department of Mathematics and Systems Analysis Series Aalto University publication series DOCTORAL DISSERTATIONS 89/2013 Field of research Mathematical analysis Manuscript submitte...

We extend the basic phase field model to physical problems in which fluid properties, such as velocity, pressure and density variations, are incorporated along with heat properties within the context of a unified and consistent derivation. One thereby obtains a system of parabolic differential equations with the variables temperature, phase, fluid velocity, density and pressure. The constants i...

We define and analyze a linear transformation – the heat transform – that allows to map solutions of hyperbolic equations to solutions of corresponding parabolic equations. The inversion of this mapping can be used to transform an inverse problem for the heat equation to a similar problem for the wave equation. This work is motivated by problems of finding interfaces, boundaries and associated ...

-Deterioration in heat transfer at supercritical water cooling in a vertical pipe is numerically analyzed. The calculation is based on a parabolic solver for steady-state equations in r-z two dimensions, a Ice model for turbulence and a steam table library for physical properties of supercritical water. Calculation results agree with the experimental data of Yamagata et al. It is found that hea...

In this paper, we consider the cost of null controllability for a large class of linear equations of parabolic or dispersive type in one space dimension in small time. By extending the work of Tenenbaum and Tucsnak in New blow-up rates for fast controls of Schrödinger and heat equations, we are able to give precise upper bounds on the time-dependance of the cost of fast controls when the time o...

The weak formulation of moving boundary problems with possibly vanishing specific heat, that is governed by parabolic and/or elliptic differential equations, is developed. The uniqueness of the resulting weak solution is then proved. This approach is used to obtain numerical solutions to some physical examples, which arise in electrochemical machining processes, and in saturated / unsaturated f...