Colombeau generalized functions and solvability of differential operators

被引：0

作者：

Benmeriem, Khaled ^{[1
]}

Bouzar, Chikh ^{[1
]}

机构：

[1] Ctr Univ Mascara, Mascara, Algeria

来源：

ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN | 2006年 / 25卷 / 04期

关键词：

Colombeau generalized functions; regularized derivatives; Mizohata type operators; solvability of differential operators;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to prove that the well known non solvable Mizohata type partial differential equations have Colombeau generalized solutions which are distributions if and only if they are solvable in the space of Schwartz distributions. Therefore the Colombeau generalized solvability includes both a new solution concept and new mathematical objects as solutions.

引用

页码：467 / 477

页数：11

共 50 条

[31] The quasiasymptotic expansion at zero and generalized Watson lemma for Colombeau generalized functions
Pilipovic, S
Stojanovic, M
Nikolic-Despotovic, D
PUBLICATIONES MATHEMATICAE DEBRECEN, 2000, 57 (1-2): : 11 - 23
[32] Composition for a class of generalized functions in Colombeau's theory
Villarreal, F
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2001, 11 (01) : 93 - 100
[33] Fourier analysis on Colombeau's algebra of generalized functions
Soraggi, RL
JOURNAL D ANALYSE MATHEMATIQUE, 1996, 69 : 201 - 227
[34] On the Generalized Stochastic Dirichlet Problem-Part II: Solvability, Stability and the Colombeau Case
Pilipovic, Stevan
Selesi, Dora
POTENTIAL ANALYSIS, 2010, 33 (03) : 263 - 289
[35] On the normal solvability and the index of differential operators
Ismailov, ZI
DOKLADY MATHEMATICS, 2000, 62 (03) : 357 - 358
[36] ALGEBRAIC AND GEOMETRIC THEORY OF THE TOPOLOGICAL RING OF COLOMBEAU GENERALIZED FUNCTIONS
Aragona, J.
Juriaans, S. O.
Oliveira, O. R. B.
Scarpalezos, D.
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2008, 51 : 545 - 564
[37] Division problem and partial differential equations with constant coefficients in Colombeau's space of new generalized functions
Nedeljkov, M
Pilipovic, S
Sad, N
Scarpalezos, D
MONATSHEFTE FUR MATHEMATIK, 1996, 122 (02): : 157 - 170
[38] Solvability Theory for Singular Integro-Differential Equations in the Class of Generalized Functions
Gabbasov, N. S.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2025, 65 (01) : 89 - 101
[39] Nonlinear generalized sections and vector bundle homomorphisms in Colombeau spaces of generalized functions
Nigsch, Eduard A.
MATHEMATISCHE NACHRICHTEN, 2017, 290 (13) : 1991 - 2008
[40] A concise introduction to Colombeau generalized functions and their applications in classical electrodynamics
Gsponer, Andre
EUROPEAN JOURNAL OF PHYSICS, 2009, 30 (01) : 109 - 126

← 1 2 3 4 5 →