Closed-Form Solutions of the Nonlinear Partial Differential Equations Governing the Stress-Field in a Rigid, Perfectly-Plastic Body

1989 ◽  
Vol 49 (5) ◽  
pp. 1374-1389 ◽  
Author(s):  
Dimitrios E. Panayotounakos ◽  
Basilios Zisis
Keyword(s):  
Partial Differential Equations ◽  
Stress Field ◽  
Differential Equations ◽  
Closed Form ◽  
Nonlinear Partial Differential Equations ◽  
Plastic Body ◽  
Partial Differential ◽  
Closed Form Solutions ◽  
Perfectly Plastic

TRANSIENT ANALYSIS OF IMMIGRATION BIRTH–DEATH PROCESSES WITH TOTAL CATASTROPHES

2003 ◽  
Vol 17 (1) ◽  
pp. 83-106 ◽  
Author(s):  
Xiuli Chao ◽  
Yuxi Zheng
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Closed Form ◽  
Stochastic Systems ◽  
Equilibrium Distribution ◽  
Partial Differential ◽  
Equilibrium Behavior ◽  
Closed Form Solutions ◽  
Population Process ◽  
Transient Solutions

Very few stochastic systems are known to have closed-form transient solutions. In this article we consider an immigration birth and death population process with total catastrophes and study its transient as well as equilibrium behavior. We obtain closed-form solutions for the equilibrium distribution as well as the closed-form transient probability distribution at any time t ≥ 0. Our approach involves solving ordinary and partial differential equations, and the method of characteristics is used in solving partial differential equations.

scholarly journals F-Operators for the Construction of Closed Form Solutions to Linear Homogenous PDEs with Variable Coefficients

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 918
Author(s):  
Zenonas Navickas ◽  
Tadas Telksnys ◽  
Romas Marcinkevicius ◽  
Maosen Cao ◽  
Minvydas Ragulskis
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Closed Form ◽  
Analytic Solutions ◽  
Variable Coefficients ◽  
Partial Differential ◽  
Computational Framework ◽  
Closed Form Solutions

A computational framework for the construction of solutions to linear homogenous partial differential equations (PDEs) with variable coefficients is developed in this paper. The considered class of PDEs reads: ∂p∂t−∑j=0m∑r=0njajrtxr∂jp∂xj=0 F-operators are introduced and used to transform the original PDE into the image PDE. Factorization of the solution into rational and exponential parts enables us to construct analytic solutions without direct integrations. A number of computational examples are used to demonstrate the efficiency of the proposed scheme.

Lyapunov-type inequalities for partial differential equations with 𝑝-Laplacian

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Robert Stegliński
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Nonlinear Partial Differential Equations ◽  
Dirichlet Boundary Conditions ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Lyapunov Inequalities ◽  
Funct Anal

Abstract The aim of this paper is to extend results from [A. Cañada, J. A. Montero and S. Villegas, Lyapunov inequalities for partial differential equations, J. Funct. Anal. 237 (2006), 1, 176–193] about Lyapunov-type inequalities for linear partial differential equations to nonlinear partial differential equations with 𝑝-Laplacian with zero Neumann or Dirichlet boundary conditions.

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