in this paper, a nonlinear inverse problem of parabolic type, is considered. by reducing this inverse problem to a system of volterra integral equations the existence, uniqueness, and stability of the solution will be shown.

An overview will be given of some nonlinear parabolic-like evolution problems which are oo the classical beaten track, but have increased in importance during the past decade. The emphasis is on problems which are nonlocal, pattern-forming (including exhibiting propagative phenomena), and/or lead in some singular limit to free boundary problems. In all cases they have been proposed as models fo...

In this paper, a positive definite semi-discrete mixed finite element method was presented for two-dimensional parabolic equations. In the new positive definite systems, the gradient equation and flux equations were separated from their scalar unknown equations.  Also, the existence and uniqueness of the semi-discrete mixed finite element solutions were proven. Error estimates were also obtaine...

In this talk, starting with some earlier results, we propose and analyze an alternate approach of optimal L2error estimates for semidiscrete Galerkin approximations to a second order linear parabolic initial and boundary value problem with rough initial data. Our analysis is based on energy arguments without using parabolic duality. Further, it follows the spirit of the proof technique used for...

A parabolic dish microphone is like a mirror telescope for sound. A parabolic reflector is used to collect and focus sound waves to a microphone receiver [1, 2]. The parabolic shape has the property that all sound waves impinging parallel to the central axis of the dish are reflected to its focus point. When the dish is aimed at a distant sound source it is safe to assume that all the sound wav...

This paper presents a sound-source-direction estimation method using only a single microphone with a parabolic reflection board. A simple signal-power-based method using a parabolic antenna has been proposed in the radar field. But the signal-power-based method is not effective for finding the direction of a talking person due to the varying power of the uttered speech signals. In this paper, t...

Let Γ be a Fuchsian group of the first kind acting on the hyperbolic upper half plane H, and let M = Γ\H be the associated finite volume hyperbolic Riemann surface. If γ is parabolic, there is an associated (parabolic) Eisenstein series, which, by now, is a classical part of mathematical literature. If γ is hyperbolic, then, following ideas due to Kudla-Millson, there is a corresponding hyperbo...

Extending our previous work in the strictly parabolic case, we show that a linearly unstable Lax-type viscous shock solution of a general quasilinear hyperbolic–parabolic system of conservation laws possesses a translation-invariant center stable manifold within which it is nonlinearly orbitally stable with respect to small L1 ∩ H3 perturbations, converging time-asymptotically to a translate of...

To solve numerically boundary value problems for parabolic equations with mixed derivatives, the construction of difference schemes with prescribed quality faces essential difficulties. In parabolic problems, some possibilities are associated with the transition to a new formulation of the problem, where the fluxes (derivatives with respect to a spatial direction) are treated as unknown quantit...

A new method of optimization on linear parabolic solar collectors using exergy analysis is presented. A comprehensive mathematical modeling of thermal and optical performance is simulated and geometrical and thermodynamic parameters were assumed as optimization variables. By applying a derived expression for exergy efficiency, exergy losses were generated and the optimum design and operating co...