The heat equation is a partial differential equation that describes the temperature of a substance as a function that varies with time. This equation, solved under certain initial and boundary ...

where u(x, y, t) is the temperature field that varies in space and time, and α is thermal diffusivity constant. The two dimensional Laplacian can be discretized with finite differences as Given an ...

In this paper we apply the Fourier transform to prove the Hyers-Ulam-Rassias stability for one dimensional heat equation on an infinite rod. Further, the paper investigates the stability of heat ...

Continuing the heat transfer series, in this video we take a look at conduction and the heat equation. Fourier's law is used to calculate the rate at which heat is transferred through an object due to ...

Blow-up solutions in semilinear heat equations refer to phenomena where solutions become unbounded in finite time, an occurrence that has far‐reaching implications for the study of nonlinear partial ...

Abstract: In this article, a novel control strategy namely disturbance observer-based control is first applied to stabilization and disturbance rejection for an antistable stochastic heat equation ...