The heat equation with Lévy noise1

The Heat Equation

Solution for the Heat Equation

Control of 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...

Generalized Gross heat equation with noises

In this paper we study the Gross heat equation perturbed by noises with the initial condition being a generalized function. The noises are given by either a white noise or a space-time white noise. The main technique we use is the representation of the Gross Laplacian as a convolution operator. It enables us to apply the convolution calculus on a suitable distribution space to obtain the explic...