scholarly journals A non-existence result for nonlinear parabolic equations with singular measures as data

2009 ◽  
Vol 139 (2) ◽  
pp. 381-392 ◽  
Author(s):  
Francesco Petitta
Keyword(s):  
Laplace Operator ◽  
Lower Order ◽  
Parabolic Equations ◽  
Existence Result ◽  
Nonlinear Parabolic Equations ◽  
Parabolic Problems ◽  
Singular Measures ◽  
Nonlinear Parabolic ◽  
Image Position ◽  
Lower Order Terms

In this paper we prove a non-existence result for nonlinear parabolic problems with zero lower-order terms whose model iswhere Δp=div(|∇u|p−2∇u) is the usual p-laplace operator, λ is measure concentrated on a set of zero parabolic r-capacity (1<p<r) and q is large enough.

EXISTENCE RESULT FOR NONLINEAR PARABOLIC EQUATIONS WITH LOWER ORDER TERMS

2011 ◽  
Vol 09 (02) ◽  
pp. 161-186 ◽  
Author(s):  
ROSARIA DI NARDO ◽  
FILOMENA FEO ◽  
OLIVIER GUIBÉ
Keyword(s):  
Laplace Operator ◽  
Lower Order ◽  
Parabolic Equations ◽  
Existence Result ◽  
Nonlinear Parabolic Equations ◽  
Parabolic Problems ◽  
Bounded Subset ◽  
Renormalized Solution ◽  
Nonlinear Parabolic ◽  
Lower Order Terms

In this paper, we prove, the existence of a renormalized solution for a class of nonlinear parabolic problems whose prototype is [Formula: see text] where QT = Ω × (0, T), Ω is an open and bounded subset of ℝN, N ≥ 2, T > 0, Δp is the so called p-Laplace operator, [Formula: see text], c ∈ (Lr(QT))N with [Formula: see text], [Formula: see text], b ∈ LN+2, 1(QT), f ∈ L1(QT), g ∈ (Lp'(QT))N and u0 ∈ L1(Ω).

scholarly journals Renormalized solutions for nonlinear parabolic problems with L1−data in orlicz-sobolev spaces

2017 ◽  
Vol 35 (1) ◽  
pp. 57 ◽  
Author(s):  
Youssef El hadfi ◽  
Abdelmoujib Benkirane ◽  
Mostafa El moumni
Keyword(s):  
Sobolev Spaces ◽  
Lower Order ◽  
Parabolic Equations ◽  
Existence Result ◽  
Nonlinear Parabolic Equations ◽  
Parabolic Problems ◽  
Renormalized Solutions ◽  
L1 Data ◽  
Nonlinear Parabolic ◽  
Lower Order Terms

In this work, we prove an existence result of renormalized solutions in Orlicz-Sobolev spaces for a class of nonlinear parabolic equations with two lower order terms and L1-data. 

scholarly journals Existence of solutions for some strongly nonlinear parabolic problems involving lower order terms in divergence form in Musielak-Orlicz spaces

2019 ◽  
Vol 38 (6) ◽  
pp. 99-126
Author(s):  
Abdeslam Talha ◽  
Abdelmoujib Benkirane
Keyword(s):  
Lower Order ◽  
Parabolic Equations ◽  
Existence Of Solutions ◽  
Orlicz Spaces ◽  
Nonlinear Parabolic Equations ◽  
Parabolic Problems ◽  
Strongly Nonlinear ◽  
L1 Data ◽  
Nonlinear Parabolic ◽  
Lower Order Terms

In this work, we prove an existence result of entropy solutions in Musielak-Orlicz-Sobolev spaces for a class of nonlinear parabolic equations with two lower order terms and L1-data.

scholarly journals Uniqueness of renormalized solutions to nonlinear parabolic problems with lower-order terms

2013 ◽  
Vol 143 (6) ◽  
pp. 1185-1208 ◽  
Author(s):  
Rosaria Di Nardo ◽  
Filomena Feo ◽  
Olivier Guibé
Keyword(s):  
Parabolic Equations ◽  
Dirichlet Boundary ◽  
Growth Conditions ◽  
Dirichlet Boundary Conditions ◽  
Parabolic Problems ◽  
Renormalized Solutions ◽  
Uniqueness Results ◽  
Nonlinear Parabolic ◽  
Image Position ◽  
Lower Order Terms

We consider a general class of parabolic equations of the typewith Dirichlet boundary conditions and with a right-hand side belonging to L1 + Lp′ (W−1, p′). Using the framework of renormalized solutions we prove uniqueness results under appropriate growth conditions and Lipschitz-type conditions on a(u, ∇u), K(u) and H(∇u).

Existence results for a class of nonlinear parabolic equations with two lower order terms

2014 ◽  
Vol 41 (2) ◽  
pp. 207-219
Author(s):  
Ahmed Aberqi ◽  
Jaouad Bennouna ◽  
M. Hammoumi ◽  
Mounir Mekkour ◽  
Ahmed Youssfi
Keyword(s):  
Lower Order ◽  
Parabolic Equations ◽  
Nonlinear Parabolic Equations ◽  
Existence Results ◽  
Nonlinear Parabolic ◽  
Lower Order Terms

Existence of bounded solutions of some nonlinear parabolic equations

1987 ◽  
Vol 107 (3-4) ◽  
pp. 313-326 ◽  
Author(s):  
A. Mokrane
Keyword(s):  
Parabolic Equations ◽  
Upper And Lower Solutions ◽  
Nonlinear Parabolic Equations ◽  
Parabolic Problems ◽  
Bounded Solutions ◽  
Open Set ◽  
Nonlinear Parabolic ◽  
Carathéodory Functions ◽  
Characteristic Features ◽  
Image Position

SynopsisThis paper proves the existence of (at least) one solution of the following equation:Here, is an elliptic operator of Leray-Lions type acting from into Lp′(0, T; W−1.p′ (Ω)), (1/p + 1/p′ = 1) and |F(u, ∇u)| ≧b(|u|)(l + |≧u|P). There are no smoothness assumptions on the bounded open set Ω; the operator and the nonlinearity F(u, ∇u) are denned in terms of Carathéodory functions. These points are the most characteristic features of this paper.Assuming the existence of upper and lower solutions allows us to obtain L∞(Q)-estimates. An estimate is then proved. The final step is to prove the strong convergence in of the approximations. This proof relies on the method introduced by L. Boccardo, F. Murat and J. P. Puel for elliptic and parabolic problems of this type.

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