Problem For Heat Equation Research Articles

Determination of an unknown radiation term in an inverse problem of heat equation

A linear conduction equation with radiative boundary condition is considered, in which the function representing radiative flux is unknown, and is to be determined from overspecified data. Exact and approximate explicit solutions are presented for the temperature and radiation term. Some uniqueness and stability results are presented. Finally some numerical results will be given.

An inverse source problem for heat equation

Several inverse problems for the heat equation in a noncylindrical domain are studied. The unknown source function f is recovered under different assumptions on the smoothness of input data and f itself. The typical problem is reduced to the system of Volterra linear integral equations. The integral transform technique is used to establish the uniqueness theorems.

Infinite-Order Differential Equations and the Heat Equation

A method is given for solving certain infinite-order differential equations whose characteristic function is an entire function of order less than 1. The infinite-order operator is expressed as an infinite product of first-order operators and is then inverted by a sequence of integral operators. The method is a natural generalization of a finite-order method and can be computed numerically. The method is shown to converge and an error estimate is given. Applications to solutions of some heat equation problems are indicated.

Inverse problems for heat equations on compact intervals and on circles, I

Inverse problems for heat equations on compact intervals and on circles, I

A Difference Scheme for Solving Two Phase Stefan Problem of Heat Equation

A Difference Scheme for Solving Two Phase Stefan Problem of Heat Equation

Intermediate Time Behavior of a Heat Equation Problem

Intermediate Time Behavior of a Heat Equation Problem

Intermediate Time Behavior of a Heat Equation Problem

section. We also assume the bar is in standard position with the x-axis along the axis of the bar and the ends at x = 0 and x = 1. Let u = u(x, t) be the temperature of the bar where x is position and t is time, and let a2 be the thermal diffusivity constant of the bar. The temperature of the bar is determined by the heat conduction equation a 2u = ut for 0 0, and the side conditions. The side conditions we shall consider are the initial condition u(x, 0) = b for 0 0. In other words, the bar is heated to a uniform temperature b; at time t = 0 the left end is changed to a temperature of 0 while the right end is changed to temperature a, and these end temperatures are then maintained. To simplify the discussion we shall assume a > 0 and 0 < b < a/2. The solution to this problem may be found in many texts such as [1] or [2]. Clearly the steady-state temperature distribution is limt u(x, t) = (a/l) x. If the temperature of the bar is plotted as a function of x for different times t, then a reasonable guess as to the intermediate time behavior of the solution is shown in FIGURE 1. Surprisingly, this behavior only occurs in the special case where b = a/2. If 0 < b < a/2, then for any x where 0 < x < bl/a (where the initial temperature is greater than the steady-state temperature), substitution of large values of t into the solution for that x results in temperatures lower than the steady-state value. For 0 < b < a/2, even where the initial temperature is greater than steady-state, the temperature of the bar will converge to the steady-state value from below. To verify and understand this behavior we must examine the solution of the problem. The

Weak periodic solutions of the boundary value problem for nonlinear heat equation

Weak periodic solutions of the boundary value problem for nonlinear heat equation

Monotonicity in a stefan problem for the heat equation

A theorem on differential inequalities related to a simple parabolic free boundary value problem is presented. The result can be used for the construction of pointwise upper and lower bounds of the free boundary curve.

On the growing up problem for semilinear heat equations

On the growing up problem for semilinear heat equations

On Generalized Heat Polynomials

The concept of a heat polynomial defined earlier by Rosenbloom and Widder is extended and the polynomials are characterized using integrals of Poisson type. One particular class of polynomials is examined in detail and leads to expansions of solutions of the problem \[u_{xx} = u_t ,\qquad u(x,0) = f(x)\] which are different from those obtained by Rosenbloom and Widder. In the last section some applications of polynomials to heat equation problems are given. In most results, much use is made of the close relationship between these polynomials and Hermite polynomials.

Stefan-Type Free Boundary Problems for Heat Equations

Stefan-Type Free Boundary Problems for Heat Equations