Non linear second order partial differential equations as generalized inverse moment problems

被引：1

作者：

Betriz Pintarelli, Maria ^{[1
,2
]}

Vericat, Fernando ^{[1
,3
]}

机构：

[1] UNLP, GAMEFI, La Plata, Buenos Aires, Argentina

[2] Univ Nacl La Plata, Dept Matemat, La Plata, Buenos Aires, Argentina

[3] UNLP, CONICET La Plata, Inst Fis Liquidos & Sistemas Biol IFLYSIB, La Plata, Buenos Aires, Argentina

来源：

JOURNAL OF INTERDISCIPLINARY MATHEMATICS | 2018年 / 21卷 / 01期

关键词：

Nonlinear PDEs; Fredholm integral equations; generalized moment problem;

D O I：

10.1080/09720502.2014.962823

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

General forms for non linear elliptic, hyperbolic and parabolic partial differential equations are considered. For all these we present a general procedure that transforms they into a Fredholm integral equation of the first kind. The resulting integral equations are then handled as a generalized moment problem. An inversion algorithm as well as conditions for the stability for the solution of this last are given. Some examples show the accuracy of the inversion method.

引用

页码：59 / 81

页数：23

共 50 条

[21] A Note on Meromorphic Solutions of Linear Partial Differential Equations of Second Order
Hu, Pei-Chu
Li, Bao Qin
COMPLEX ANALYSIS AND OPERATOR THEORY, 2014, 8 (06) : 1173 - 1182
[22] Fundamental solutions for second order linear elliptic partial differential equations
Clements, DL
COMPUTATIONAL MECHANICS, 1998, 22 (01) : 26 - 31
[23] Global Solutions of Homogeneous Linear Partial Differential Equations of the Second Order
Hu, Pei-Chu
Yang, Chung-Chun
MICHIGAN MATHEMATICAL JOURNAL, 2009, 58 (03) : 807 - 831
[24] A Note on Meromorphic Solutions of Linear Partial Differential Equations of Second Order
Pei-Chu Hu
Bao Qin Li
Complex Analysis and Operator Theory, 2014, 8 : 1173 - 1182
[25] Normal forms of linear second order partial differential equations on the plane
Alexey Davydov
Science China Mathematics, 2018, 61 : 1947 - 1962
[26] Taylor polynomial solutions of second order linear partial differential equations
Kesan, C
APPLIED MATHEMATICS AND COMPUTATION, 2004, 152 (01) : 29 - 41
[27] Fundamental solutions for second order linear elliptic partial differential equations
D. L. Clements
Computational Mechanics, 1998, 22 : 26 - 31
[28] Normal forms of linear second order partial differential equations on the plane
Davydov, Alexey
SCIENCE CHINA-MATHEMATICS, 2018, 61 (11) : 1947 - 1962
[29] Boundary value problems for second order linear difference equations: application to the computation of the inverse of generalized Jacobi matrices
Encinas, A. M.
Jimenez, M. J.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2019, 113 (04) : 3795 - 3828
[30] Parametric factorization of non linear second order differential equations
Contreras, Gabriel Gonzalez
PHYSICA SCRIPTA, 2024, 99 (05)

← 1 2 3 4 5 →