Saksida, Grega

Toplotna enačba je ena najpomembnejših parcialnih diferencialnih enačb v matematiki in naravoslovju. Njene rešitve se navadno ne da izraziti v zaprti eksplicitni obliki, jo pa lahko zapišemo v integralski obliki z uporabo t. i. fundamentalne rešitve ali pa kot neskončno vrsto rešitev lastnega problema, če jo rešujemo na omejeni množici. V tej magis...

Popa, Vlad (author)

In an attempt to find alternatives for solving partial differential equations (PDEs)

with traditional numerical methods, a new field has emerged which incorporates

the residual of a PDE into the loss function of an Artificial Neural Network. This

method is called Physics-Informed Neural Network (PINN). In this thesis, we study dense neural networks (D...

Duprez, Michel Lleras, Vanessa Lozinski, Alexei Vuillemot, Killian

Thanks to a finite element method, we solve numerically parabolic partial differential equations on complex domains by avoiding the mesh generation, using a background regular mesh, not fitting exactly the domain and the real boundary of the domain like immersed boundary methods. Our technique follows the ϕ-FEM paradigm which suppose that the domai...

Mosa, Gamal A. Abdou, Mohamed A. Gawish, Fatma A. Abdalla, Mostafa H.
Published in
Mathematica Slovaca

In this paper, the semi-group method is used to discuss the existence and uniqueness of solutions for fractional and partial integro differential equations (F-PIDEs) of heat type in Banach space E. In addition, the stability of the solutions for F-PIDEs are discussed. Moreover, the Adomian decomposition method (ADM) is used to obtain the solutions ...

Xue, Xiaofeng Zhao, Linjie

We introduce the voter model on the infinite lattice with a slow membrane and investigate its hydrodynamic behavior. The model is defined as follows: a voter adopts one of its neighbors' opinion at rate one except for neighbors crossing the hyperplane {x : x 1 = 1/2}, where the rate is αN −β. Above, α > 0, β ≥ 0 are two parameters and N is the scal...

p., grigorios

Introduction: Heat is a kinetic process whereby energy flows from between two systems, hot-to-cold objects. In oro-dental implantology, conductive heat transfer/(or thermal stress) is a complex physical phenomenon to analyze and consider in treatment planning. Hence, ample research has attempted to measure heat-production to avoid over-heating duri...

Iwasaki, Satoru
Published in
Inverse Problems

This paper deals with initial state estimation problems of the heat equation in equilateral metric graphs being admitted to have cycles. Particularly, we are concerned with suitable placements of observation points in order to uniquely determine the initial state from observation data. We give a necessary and sufficient condition for suitable place...

Guillot, Jules Frénod, Emmanuel Ailliot, Pierre

Data assimilation consists in combining a dynamical model with noisy observations to estimate the latent true state of a system. The dynamical model is generally misspecified and this generates a model error which is usually treated using a random noise. The aim of this paper is to suggest a new treatment for the model error that further takes into...

Kosmakova, M. T. Ramazanov, M. I. Kasymova, L. Zh.
Published in
Lobachevskii Journal of Mathematics

AbstractIn the paper, a boundary value problem for a fractionally loaded heat equations is considered in the first quadrant. The questions of the existence and uniqueness of the solution are investigated in the class of continuous functions. The loaded term has the form of the Caputo fractional derivative with respect to the spatial variable, and, ...

Denisov, A. M.
Published in
Computational Mathematics and Mathematical Physics

AbstractFor the heat conduction equation with a singular perturbation corresponding to a small heat capacity or a small heat conductivity, inverse problems of determining the boundary or initial condition or the source term from additional information about the solution of the equation are considered. The possibility of using the expansion in a sma...