Existence of renormalized solutions to a nonlinear parabolic boundary value problem with a singular lower order term and a nonhomogeneous datum

被引：0

作者：

Abdellaoui M. ^{[1
,2
]}

机构：

[1] LAMA, Department of Mathematics, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Atlas Fez

[2] Faculté des Sciences Juridiques, Économiques et Sociales, Université Hassan 1, Settat

来源：

ANNALI DELL'UNIVERSITA' DI FERRARA | 2023年 / 69卷 / 1期

关键词：

Measures & capacities; Singular parabolic equations; Smoothness and regularity of solutions; Weak/renormalized solutions;

D O I：

10.1007/s11565-022-00426-5

中图分类号：

学科分类号：

摘要：

We study existence and uniqueness results for nonlinear parabolic equations with possibly singular lower order term and nonregular datum of the the following form (P){ut-Δpu=H(u)μinQ:=(0,T)×Ω,u(t,x)>0inQ,u(t,x)=0on(0,T)×∂Ω,u(t,x)=u0(x)in{0}×Ω,where Ω is an open bounded subset of RN (N≥ 2), T> 0 , Δ pu: = div (| ∇ u| p-2∇ u) (1 < p< N) is the p-Laplace operator, u is an integrable function and μ is a bounded Radon measure data. The term H is a nonnegative continuous and finite function outside the origin, which, roughly speaking, behaves as s-γ (γ≥ 0) near zero. © 2022, The Author(s) under exclusive license to Università degli Studi di Ferrara.

引用

页码：273 / 314

页数：41

共 50 条

[1] Existence and Uniqueness of Renormalized Solutions for a Nonlinear p(x)-Parabolic Problem With Lower Order Term and General Data
Sabiry, Abdelaziz
Zineddaine, Ghizlane
Kassidi, Abderrazak
Melliani, Said
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2025,
[2] Existence and Uniqueness of Renormalized Solutions to Nonlinear Parabolic Equations with Lower Order Term and Diffuse Measure Data
Bouajaja, A.
Redwane, H.
Marah, A.
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2018, 15 (04)
[3] Existence and Uniqueness of Renormalized Solutions to Nonlinear Parabolic Equations with Lower Order Term and Diffuse Measure Data
A. Bouajaja
H. Redwane
A. Marah
Mediterranean Journal of Mathematics, 2018, 15
[4] Existence of Positive Solutions of a Singular Nonlinear Boundary Value Problem
Ma, Ruyun
Li, Jiemei
BOUNDARY VALUE PROBLEMS, 2010,
[5] Existence of Positive Solutions of a Singular Nonlinear Boundary Value Problem
Ruyun Ma
Jiemei Li
Boundary Value Problems, 2010
[6] Existence of positive solutions to a singular second order boundary value problem
Kelevedjiev, P
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2002, 50 (08) : 1107 - 1118
[7] THE EXISTENCE OF POSITIVE SOLUTIONS TO A SINGULAR NONLINEAR BOUNDARY-VALUE PROBLEM
WANG, JY
JIANG, J
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1993, 176 (02) : 322 - 329
[8] EXISTENCE OF SOLUTIONS OF A NONLINEAR THIRD ORDER BOUNDARY VALUE PROBLEM
Guezane-Lakoud, Assia
Frioui, Assia
FIXED POINT THEORY, 2012, 13 (02): : 501 - 506
[9] Existence of generalized solutions for a nonhomogeneous boundary value problem
Sun, Yingfei
Zhou, Meike
Fan, Tianyou
Hsi-An Chiao Tung Ta Hsueh/Journal of Xi'an Jiaotong University, 1998, 32 (09): : 210 - 214
[10] Existence of a Renormalized Solution of Nonlinear Parabolic Equations with Lower Order Term and General Measure Data
Marah, A.
Bouajaja, A.
Redwane, H.
BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2021, 39 (03): : 93 - 114

← 1 2 3 4 5 →