This paper is concerned with the null-exact controllability of a cascade system formed by a semilinear heat and a semilinear wave equation in a cylinder Ω×(0, T ). More precisely, we intend to drive the solution of the heat equation (resp. the wave equation) exactly to zero (resp. exactly to a prescribed but arbitrary final state). The control acts only on the heat equation and is supported by ...

Rate of heat transfer ∂u = (1) −K0 area ∂x where K0 is the thermal conductivity, units [K0] = MLT U . In other words, heat is transferred from areas of high temp to low temp. 3. Conservation of energy. Consider a uniform rod of length l with non-uniform temperature lying on the x-axis from x = 0 to x = l. By uniform rod, we mean the density ρ, specific heat c, thermal conductivity K0, cross-sec...

Rapid processes of heat transfer are not described by the standard heat conduction equation. To take into account a finite velocity of heat transfer, we use the hyperbolic model of heat conduction, which is connected with the relaxation of heat fluxes. In this case, the mathematical model is based on a hyperbolic equation of second order or a system of equations for the temperature and heat flu...

a modification of peng-robinson equation is described wherein in the parameter b is expressed as a linear function of temperature. the modified equation is then applied to a series of light hydrocarbons and refrigerants, and predicted values for vapor pressure, saturated vapor volume, saturated liquid volume and the heat of evaporation are compared with the corresponding experimental data. cons...

this work concerns the study of existence and uniqueness to heat equation with fractional laplacian dierentiation in extended colombeau algebra.

A Bäcklund transformation(BT) and a recurrence formula are derived by the homogeneous balance(HB) method. A initial problem of Burgers equations is reduced to a initial problem of heat equation by the BT, the initial problem of heat equation is resolved by the Fourier transformation method, substituting various solutions of the initial problem of the heat equation will yield solutions of the in...

Abstract: A one dimensional heat equation in a semi-infinite medium controlled through a heat source depending on the delayed heat flux at the extremum is studied. By reducing the problem to a delayed Volterra integral equation with a weakly singular kernel, we find conditions on the initial datum and on the source term of the equation to control the asymptotic behaviour of the mean temperatures.

This paper deals with a numerical method for the solution of the heat equation with nonlinear nonlocal boundary conditions. Here nonlinear terms are approximated by Richtmyer’s linearization method. The integrals in the boundary equations are approximated by the composite Simpson rule. A difference scheme is considered for the one-dimensional heat equation. In final part, the numerical results ...