Hyperbolicity of the heat equation

The Heat Equation

Control of the Heat Equation

Semi-hyperbolicity and Hyperbolicity

We prove that for C1-diffeomorfisms semi-hyperbolicity of an invariant set implies its hyperbolicity. Moreover, we provide some exact estimations of hyperbolicity constants by semi-hyperbolicity ones, which can be useful in strict numerical computations.

Solution for the Heat Equation

The 1-D Heat Equation

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...