In this paper, we establish a global Carleman estimate for stochastic parabolic equations. Based on this estimate, we solve two inverse problems for stochastic parabolic equations. One is concerned with a determination problem of the history of a stochastic heat process through the observation at the final time T , for which we obtain a conditional stability estimate. The other is an inverse so...

In this paper, we construct some interesting Gevrey functions of order α for every α > 1 with compact support by a clever use of the Bray-Mandelbrojt iterative process. We then apply these results to the moment method, which will enable us to derive some upper bounds for the cost of fast boundary controls for a class of linear equations of parabolic or dispersive type that partially improve the...

We give the regularization for fractional integral by delta sequence and apply it to obtain existence-uniqueness theorems in Colombeau algebras for nonlinear equations with singularities: nonlinear system of integral equations with polar kernel and nonlinear parabolic equations (of ordinary type, with nonlinear conservative term and with Schrödinger kernel) with strongly singular initial data a...

Elliptic equations: 1. Harmonic functions 2. Perron’s method 3. Potential theory 4. Existence results; the method of suband supersolutions 5. Classical maximum principles for elliptic equations 6. More regularity, Schauder’s theory for general elliptic operators 7. The weak solution approach in one space dimension 8. Eigenfunctions for the Sturm-Liouville problem 9. Generalization to more dimen...

The study of flow and heat transfer over rotating circular disks is of great practical importance in understanding the cooling of rotatory machinery such as turbines, electric motors and design and manufacturing of computer disk drives. This paper presents an analysis of the flow and heat transfer over a heated infinite permeable rough disk. Boundary-layer approximation reduces the elliptic Nav...

Inverse Heat Conduction Problems (abbr.: IHCP) occur whenever surface temperatures and surface heat fluxes should be determined at inaccessible portions of the surface from corresponding measurements at accessible parts. These problems are known to be severely illposed. There are various approaches to regularize and stabilize the illposedness (see [4, 11, 20] and the references therein). An IHC...

this paper presents a class of theoretical and iterative method for linear partial differential equations. an algorithm and analytical solution with a initial condition is obtained using the reduced differential transform method. in this technique, the solution is calculated in the form of a series with easily computable components. there test modeling problems from mathematical mechanic, physi...

Approximation theorems, analogous to known results for linear elliptic equations, are obtained for solutions of the heat equation. Via the Cole-Hopf transformation, this gives rise to approximation theorems for a nonlinear parabolic equation, Burgers’ equation.

heat and mass transfer, in this paper, is considered in one-row heat exchanger, that fins are hotter than air flow and water is added to fins. related governing equations are derived by analyzing a two-dimension model in a unique cell of a heat exchange. these equations are numerically solved by finite difference method. heat transfer and efficiency under partially wet surface are calculated by...

Abstract: We consider three level difference replacements of parabolic equations focusing on the heat equation in two space dimensions. Through a judicious splitting of the approximation, the scheme qualifies as an alternating direction implicit (ADI) method. Using the well known fact of the parabolic-elliptic correspondence, we shall derive a two stage iterative procedure employing a fractiona...