A one parameter family of equations is considered which connects the well-known Perona-Malik equation to standard diffusion. The parameter acts as a regularization parameter which gradually modifies the ill-posed Perona-Malik equation, through a strongly locally well-posed equation, to a strongly globally well-posed one which exhibits a behavior akin to that of standard diffusion, which is itse...

For good image quality using ultrasound inverse scattering, one alternately solves the well-posed forward scattering equation for an estimated total field and the ill-posed inverse scattering equation for the desired object property function. In estimating the total field, error or noise contaminates the coefficients of both matrix and data of the inverse scattering equation. Previous work on i...

Linear equality systems with fuzzy parameters and crisp variables defined by the Zadeh’s extension principle are called possibilistic linear equality systems. This study focuses on the problem of stability (with respect to small changes in the membership function of fuzzy parameters) of the solution in these systems.

We consider the spectral truncation as regularization for an ill-posed non-homogeneous parabolic final value problem, and obtain error estimates under a general source condition when data, which consist of term well value, are noisy. The resulting estimate is compared with corresponding Lavrentieve method, showed that method has no index saturation.

The inverse geothermal problem consist of estimating the temperature distribution below the earth’s surface using temperature and heat-flux measurements on the earth’s surface. The problem is important since temperature governs a variety of the geological processes including formation of magmas, minerals, fosil fuels and also deformation of rocks. Mathematical this problem is formulated as a Ca...

We investigate the well-posedness of a class of nonlinear dispersive waves on trees, in connection with the mathematical modeling of the human cardiovascular system. Specifically, we study the Benjamin-Bona-Mahony (BBM) equation, also known as the regularized long wave equation, posed on finite trees, together with standard junction and terminal boundary conditions. We prove that the Cauchy pro...

in this article, a numerical approximation to the solution of the newell-whitehead equation (nwe) and cauchy problem of ill-posed non-linear diffusion equation have been studied. the presented scheme is obtained by using the derivative of the cubic b-spline quasi-interpolation (bsqi) to approximate the spatial derivative of the dependent variable and first order forward difference to approximat...