We consider the Cauchy problem for nonlinear parabolic equations with functional dependence represented by the Hale functional acting on the unknown function and its gradient. We prove convergence theorems for a general quasilinearization method in natural subclasses of unbounded solutions.
Centre of Applied Mathematics invites you to participate in the competition for the best work on mathematics and its applications is organized within the three-year project conducted Centre of Applied Mathematics at the Faculty of Technical Physics and Applied Mathematics, University of Gdansk. The purpose of the competition is to highlight the most significant scientific papers published in recent years.
Konkurs na najlepsze prace dotyczące matematyki i jej zastosowań organizowany jest w ramach trzyletniego projektu Centrum Zastosowań Matematyki realizowanego na Wydziale Fizyki Technicznej i Matematyki Stosowanej Politechniki Gdańskiej. Zadaniem konkursu jest wyróżnienie najbardziej doniosłych artykułów naukowych opublikowanych w ostatnich latach.
We consider the Cauchy problem for nonlinear parabolic equations with functional dependence. We prove Schauder-type existence results for unbounded solutions. We also prove existence of maximal solutions for a wide class of differential functional equations.
Abstract. Center of Applied Mathematics is the project co-financed by EuropeanUnion within the Human Capital Operational Programme. Its main aim is to promoteinterdisciplinary cooperation between mathematicians and the representativesof other disciplines as well as the development of the mathematical methods whichcould be useful in the sphere of applications. The project is realized at Faculty ofApplied Physics and Mathematics of Gdansk University o Technology. In the articlethe main tasks realized...
The phenomenon of thermal ablation is described by Pennes' bioheat equation. This model is based on Newton's law of cooling. Many approximate methods have been considered because of the importance of this issue. We propose an implicit numerical scheme which has better stability properties than other approaches.
We propose a simplified mathematical model of the hypothalamus-pituitary-thyroid (HPT) axis in an endocrine system. The considered model is a modification of the model proposed by Mukhopadhyay in [9]. Our system of delay differential equations reconstructs the HPT-axis in relation to 24h profiles of human in physiological conditions. Homeostatic control of the thyroid-pituitary axis is considered by using feedback and delay in our model. The influence of delayed feedback on the stability behaviour...
Page 1