GENERALIZED SOLUTIONS TO A NON-LIPSCHITZ GOURSAT PROBLEM

被引：0

作者：

Devoue, Victor ^{[1
]}

机构：

[1] Univ Antilles Guyane, Equipe Anal Algebr Non Lineaire Dept Sci Interfac, Campus Schoelcher BP 7209, Pointe a Pitre 97275, Guadeloupe, France

来源：

DIFFERENTIAL EQUATIONS & APPLICATIONS | 2009年 / 1卷 / 02期

关键词：

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the semilinear wave equation in canonical form with non-Lipschitz non-linearity by using the recent theories of generalized functions. We investigate solutions to the Goursat problem. We turn this non-Lipschitz Goursat problem with irregular data into a biparameter family of problems. The first parameter replaces the problem by a family of Lipschitz problems and the second one regularizes the data. Finally the family of problems is solved in an appropriate biparametric (C, E, P) algebra.

引用

页码：153 / 178

页数：26

共 50 条

[1] POSITIVE SOLUTIONS TO A DIRICHLET PROBLEM WITH NON-LIPSCHITZ NONLINEARITIES
Anello, Giovanni
[J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2021,
[2] Generalized solutions to nonlinear Volterra integral equations with non-Lipschitz nonlinearity
Pilipovic, S
Stojanovic, M
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1999, 37 (03) : 319 - 335
[3] GENERALIZED SOLUTIONS TO A NON LIPSCHITZ-CAUCHY PROBLEM
Devoue, V.
[J]. JOURNAL OF APPLIED ANALYSIS, 2009, 15 (01) : 1 - 32
[4] Positive solutions to a Kirchhoff problem with sign-changing and non-Lipschitz nonlinearities
Anello, Giovanni
Furnari, Luca
[J]. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2020, 65 (12) : 1998 - 2007
[5] TERRACE SOLUTIONS FOR NON-LIPSCHITZ MULTISTABLE NONLINEARITIES
Giletti, Thomas
Kim, Ho-Youn
Kim, Yong-Jung
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2022, 54 (04) : 4785 - 4805
[6] Semigroup theory and analysis of solutions for a higher order non-Lipschitz problem with advection in RN
Luis Diaz Palencia, Jose
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2024,
[7] Semigroup Theory and Analysis of Solutions for a Higher Order Non-Lipschitz Problem With Advection in RN
Diaz Palencia, Jose Luis
[J]. INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2022, ICNAAM-2022, 2024, 3094
[8] On an indefinite, non-Lipschitz semilinear elliptic problem: Compactly supported solutions, multiplicity and uniqueness
Lu, Qiuping
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 389 (01) : 569 - 590
[9] Regularity of solutions to differential equations with non-Lipschitz coefficients
Luo, Dejun
[J]. BULLETIN DES SCIENCES MATHEMATIQUES, 2008, 132 (04): : 257 - 271
[10] GENERALIZED GOURSAT PROBLEM
HOLTEN, RP
[J]. PACIFIC JOURNAL OF MATHEMATICS, 1962, 12 (01) : 207 - &

← 1 2 3 4 5 →