scholarly journals Mathematical analysis of a nonlinear PDE model for European options with counterparty risk

2019 ◽  
Vol 357 (3) ◽  
pp. 252-257 ◽  
Author(s):  
Iñigo Arregui ◽  
Beatriz Salvador ◽  
Daniel Ševčovič ◽  
Carlos Vázquez
Keyword(s):  
Mathematical Analysis ◽  
Nonlinear Pde ◽  
Counterparty Risk ◽  
European Options ◽  
Pde Model

scholarly journals On-line Identification of the Sine-Gordon Nonlinear PDE Model

2021 ◽  
Vol 54 (9) ◽  
pp. 458-461
Author(s):  
Yury Orlov ◽  
Oscar Gomez
Keyword(s):  
Nonlinear Pde ◽  
Pde Model ◽  
Line Identification ◽  
On Line

Mathematical Analysis of a Non-Local Mixed ODE-PDE Model for Tumor Invasion and Chemotherapy

2020 ◽  
Vol 170 (1) ◽  
pp. 415-442
Author(s):  
Anderson L. A. de Araujo ◽  
Artur C. Fassoni ◽  
Luís F. Salvino
Keyword(s):  
Mathematical Analysis ◽  
Tumor Invasion ◽  
Pde Model ◽  
Non Local

scholarly journals Diffusion–reaction compartmental models formulated in a continuum mechanics framework: application to COVID-19, mathematical analysis, and numerical study

2020 ◽  
Vol 66 (5) ◽  
pp. 1131-1152 ◽  
Author(s):  
Alex Viguerie ◽  
Alessandro Veneziani ◽  
Guillermo Lorenzo ◽  
Davide Baroli ◽  
Nicole Aretz-Nellesen ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Continuum Mechanics ◽  
Mathematical Analysis ◽  
Numerical Study ◽  
Interdisciplinary Collaboration ◽  
Compartmental Models ◽  
Diffusion Reaction ◽  
Pde Model ◽  
Fundamental Equations ◽  
Detailed Derivation

Abstract The outbreak of COVID-19 in 2020 has led to a surge in interest in the research of the mathematical modeling of epidemics. Many of the introduced models are so-called compartmental models, in which the total quantities characterizing a certain system may be decomposed into two (or more) species that are distributed into two (or more) homogeneous units called compartments. We propose herein a formulation of compartmental models based on partial differential equations (PDEs) based on concepts familiar to continuum mechanics, interpreting such models in terms of fundamental equations of balance and compatibility, joined by a constitutive relation. We believe that such an interpretation may be useful to aid understanding and interdisciplinary collaboration. We then proceed to focus on a compartmental PDE model of COVID-19 within the newly-introduced framework, beginning with a detailed derivation and explanation. We then analyze the model mathematically, presenting several results concerning its stability and sensitivity to different parameters. We conclude with a series of numerical simulations to support our findings.

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