Nonhomogeneous Heat Equation Research Articles

A model of non-homogeneous damped electromagnetic wave and heat equation in ferrite materials

This study uses a closely coupled model to treat the core loss of ferrite by the combination of non-homogeneous damped electromagnetic wave and heat equation. The heat dissipation of ferrites is caused by the core loss, which is a summation of magnetic, dielectric and eddy current losses. Explicit finite difference method solves the coupled equations to calculate core loss and compares it with the measured results. Those results show that this method can be used to analyze electromagnetic and thermal field with temperature dependence of ferrites.

Approximation of a Function by Solutions of an Underdetermined Nonhomogeneous Heat Equation

The best (in the L 2 sense) approximation of a given function by solutions of an underdetermined nonhomogeneous heat equation is considered. The problem is reduced to a well-posed boundary value problem for a fourth-order partial differential equation. The eigenfunction expansion of the solution of this well-posed problem is obtained in a one-dimensional spatial case. The found best approximation and partial sums of its eigenfunction expansion provide an enhanced approximation of any unknown temperature distribution.

Weighted sobolev spaces and the heat equation in the whole space

The Cauchy problem for the nonhomogeneous heat equation is considered. Solutions are looked for in Sobolev spaces with weights which are powers of the first coordinate.

DETERMINATION OF AN UNKNOWN NONHOMOGENEOUS TERM p(t) IN A STEFAN PROBLEM

A one-phase Stefan problem for the nonhomogeneous heat equation with the source term depending on an unknown parameter p(t) is considered. The existence and uniqueness of the solution (p, s, u) are also demonstrated.

Liouville theorems for nonlinear parabolic equations of second order

We study entire solutions (i.e., solutions defined in all of $\mathcal {R}^{n+1}$) of second-order nonlinear parabolic equations with linear principal part. Under appropriate hypotheses, we establish existence and uniqueness of an entire solution vanishing at infinity. More generally, we discuss existence and uniqueness of an entire solution approaching a given heat polynomial at infinity. When specialized to the linear homogeneous parabolic equation, containing no zero-order term, our results yield a Liouville theorem stating that an entire and bounded solution must be constant; certain asymptotic behavior of the coefficients at infinity however is required. Our methods involve the establishment of a priori bounds on entire solutions, first for the nonhomogeneous heat equation and then for a more general linear parabolic equation; we use these bounds with a Schauder continuation technique to study the nonlinear equation.

The induction of a propagating normal zone (quench) in a superconductor by local energy release

Experiments were performed to measure the minimum energy, Ec of an instantaneous point source, needed to induce a propagating normal transition (quench) in a superconductor. The energy pulse was supplied to the superconductor by a miniaturized heater element which had a thermal time constant of ∼ 20 μs. Ec depends on the current distribution in the conductor and is lower for a nonhomogeneous distribution. A computer calculation solving the nonhomogeneous heat equation agrees within a factor of two with the results for adiabatic conditions (no radial heat transfer) without adjustable parameters. The results obtained with the conductor placed in liquid helium could be fitted into the calculation with parameters close to measured transient heat transfer data.

Almost automorphic solutions of non-homogeneous heat equation

In this paper we consider the non-homogeneous heat equation with almost-automorphic right-hand side. Some results concerning bounded and almost-automorphic solutions are given.