Cauchy Problem For Heat Equation Research Articles

On recovery of the solution to the Cauchy problem for the singular heat equation

We present the results related to the solution of the problem of the best recovery of the solution to the Cauchy problem for the heat equation with the B-elliptic Laplace-Bessel operator in spatial variables from an exactly or approximately known finite set of temperature profiles.

The Cauchy problem for heat equation with fractional Laplacian and exponential nonlinearity

We consider the Cauchy problem for heat equation with fractional Laplacian and exponential nonlinearity. We establish local well-posedness result in Orlicz spaces. We derive the existence of global solutions for small initial data. We obtain decay estimates for large time in Lebesgue spaces.

A modified regularization method for a Cauchy problem for heat equation on a two-layer sphere domain

In this paper, we study a non-characteristic Cauchy problem for a radially symmetric inverse heat conduction equation in a two-layer domain. This is a severely ill-posed problem in the sense that the solution (if it exists) does not depend continuously on the data. It is well-known that the classical Tikhonov regularization solutions are too smooth and the approximate solutions may lack details that might be contained in the exact solutions. Combining Fourier transform technique with a modified version of the classical Tikhonov regularization, we obtain a regularized solution which is stably convergent to the exact solution with a sharp error estimate.

Moment Problem and Inverse Cauchy Problems for Heat Equation

The solution of Hamburger and Stieltjes moment problem can be thought of as the solution of a certain inverse Cauchy problem. The solution of the inverse Cauchy problem for heat equation is founded in the form of Hermite polynomial series. The author reveals, the formulas obtained by him for the solution of inverse Cauchy problem have a symmetry with respect to the formulas for corresponding direct Cauchy problem. Obtained formulas for solution of the inverse problems can serve as a basis for the solution of the moment problem.

Semi-discretization Difference Approximation for a Cauchy Problem of Heat Equation in Two-dimensional Space

Semi-discretization Difference Approximation for a Cauchy Problem of Heat Equation in Two-dimensional Space

Numerical Computation Based on the Method of Fundamental Solutions for a Cauchy Problem of Heat Equation

In this note, a boundary integral equation method coupled with the method of fundamental solutions for solving an inverse heat conduction problem is considered. The Tikhonov regularization method is employed for solving this system of equations. Determination of regularization parameter is based on GCV criterion. To illustrate our main results, some numerical examples are given.

The Cauchy problem for heat equations with exponential nonlinearity

The Cauchy problem for the semilinear heat equations is studied in the Orlicz space exp L 2 ( R n ) , where any power behavior of interaction works as a subcritical nonlinearity. We prove the existence of global solutions for the semilinear heat equations with the exponential nonlinearity under the smallness condition on the initial data in exp L 2 ( R n ) .

Identification of a moving boundary for a heat conduction problem in a multilayer medium

In this paper, we give a uniqueness theorem for the moving boundary of a heat problem in a composite medium. Through solving the Cauchy problem of heat equation in each subdomain, we finally find an approximation to the moving boundary for one-dimensional heat conduction problem in a multilayer medium. The numerical scheme is based on the use of the method of fundamental solutions and a discrete Tikhonov regularization technique with the generalized cross-validation choice rule for a regularization parameter. Numerical experiments for five examples show that our proposed method is effective and stable.

On necessary conditions for the stabilization with weight tv (t→∞) of the solution of the cauchy problem for heat equation

In this note we investigate the question of necessary conditions for the stabilization with weight tv (t→∞) of the Cauchy problem for the heat equation in terms of the stabilization with weight of the Stieltjes means of initial function.

On generalized functions approach to the cauchy problem for heat equation

The purpose of this paper is to solve the Cauchy problem for heat equation with tempered distributional data using an elementary method.