scholarly journals Existence Results for Doubly Nonlinear Parabolic Equations with Two Lower-Order Terms and L1-Data

2019 ◽  
Vol 71 (5) ◽  
pp. 692-717
Author(s):  
A. Benkirane ◽  
Y. El Hadfi ◽  
M. El Moumni
Keyword(s):  
Lower Order ◽  
Parabolic Equations ◽  
Nonlinear Parabolic Equations ◽  
Existence Results ◽  
L1 Data ◽  
Nonlinear Parabolic ◽  
Doubly Nonlinear ◽  
Lower Order Terms

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

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 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 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 Harnack’s inequality for doubly nonlinear equations of slow diffusion type

2021 ◽  
Vol 60 (6) ◽  
Author(s):  
Verena Bögelein ◽  
Andreas Heran ◽  
Leah Schätzler ◽  
Thomas Singer
Keyword(s):  
Vector Field ◽  
Harnack Inequality ◽  
Parabolic Equations ◽  
Full Range ◽  
Nonlinear Parabolic Equations ◽  
Growth Conditions ◽  
Diffusion Type ◽  
Slow Diffusion ◽  
Nonlinear Parabolic ◽  
Doubly Nonlinear

AbstractIn this article we prove a Harnack inequality for non-negative weak solutions to doubly nonlinear parabolic equations of the form $$\begin{aligned} \partial _t u - {{\,\mathrm{div}\,}}{\mathbf {A}}(x,t,u,Du^m) = {{\,\mathrm{div}\,}}F, \end{aligned}$$ ∂ t u - div A ( x , t , u , D u m ) = div F , where the vector field $${\mathbf {A}}$$ A fulfills p-ellipticity and growth conditions. We treat the slow diffusion case in its full range, i.e. all exponents $$m > 0$$ m > 0 and $$p>1$$ p > 1 with $$m(p-1) > 1$$ m ( p - 1 ) > 1 are included in our considerations.

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