On equations with infinitely many derivatives: integral transforms and the Cauchy problem

2nd International Conference on Mathematical Modeling in Physical Sciences 2013

物理学;数学

Prado, Humberto^1 ; Reyes, Enrique G.^1

Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Casilla 307, Correo 2 Santiago, Chile^1

关键词: Cauchy problems;    Finite number;    Half-line;    Initial conditions;    Integral transform;    Laplace operator;    Nonlinear partial differential equations;    Nonlocal;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/490/1/012044/pdf
DOI  :  10.1088/1742-6596/490/1/012044

来源: IOP

【 摘 要 】

We analyze initial value problems for ordinary differential equations with infinitely many derivatives such as (linearized versions of) nonlocal field equations of motion appearing in particle physics, nonlocal cosmology and string theory. We show that the corresponding initial value problem on a half line is well-posed and that it requires only a finite number of initial conditions. We also investigate nonlinear pseudo-equations defined by functions of the Laplace operator, that is, nonlinear partial differential equations with infinitely many derivatives.