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17
Citations
Citations since 2017
Publications
Publications (7)
This paper is concerned with an age-structured model in population dynamics. We investigate the uniqueness of solution for this type of nonlinear reaction-diffusion problem when the source term depends on the density, indicating the presence of, for example, mortality and reaction processes. Our result shows that in a spatial environment, if two po...
This paper is concerned with an age-structured model in population dynamics. We investigate the uniqueness of solution for this type of nonlinear reaction-diffusion problem when the source term depends on the density, indicating the presence of, for example, mortality and reaction processes. Our result shows that in a spatial environment, if two po...
The main goal of this paper is applying the cut-off projection for solving one-dimensional backward heat conduction problem in a two-slab system with a perfect contact. In a constructive manner, we commence by demonstrating the Fourier-based solution that contains the drastic growth due to the high-frequency nature of the Fourier series. Such insta...
Central forces play important role in the analysis of results obtained with particle simulation methods, since they allow evaluating stress fields. In this work we derive expressions for a central-force decompositon of the Tersoff potential, which is often used to describe interatomic interactions in covalently bonded materials. We simplify the obt...
This Note derives regularity bounds for a Gevrey criterion when the Cauchy problem of elliptic equations is solved by regularization. When utilizing the regularization, one knows that checking such criterion is basically problematic, albeit its importance to engineering circumstances. Therefore, coping with that impediment helps us improve the use...
Instability of ill-posed problem is one of the most interesting field in PDE models. Many approaches have been conceived in order to stabilize the solution. The main concern of this work is the cut-off projection for the one-dimensional backward heat conduction problem in a two-slab system with perfect contact. In a constructive manner, we commence...
In this paper, we study the inverse problem for a class of abstract
ultraparabolic equations which is well-known to be ill-posed. We employ some
elementary results of semi-group theory to present the formula of solution,
then show the instability cause. Since the solution exhibits unstable
dependence on the given data functions, we propose a new re...
Projects
Project (1)
We focus on designing approximation schemes for some classes of nonlinear ultra-parabolic equations with applications in population dynamics, especially in cancer growth with standard mechanisms. On the other hand, the weak solvability results are interesting in this direction. This type of problems is somewhat applicable in multiparameter Brownian motion and heat transfer with multi-phenomena.
