Doubly nonlinear parabolic equations with singular lower order term

2004 ◽  
Vol 56 (2) ◽  
pp. 185-199 ◽  
Author(s):  
Ismail Kombe
Keyword(s):  
Lower Order ◽  
Parabolic Equations ◽  
Order Term ◽  
Nonlinear Parabolic Equations ◽  
Lower Order Term ◽  
Nonlinear Parabolic ◽  
Doubly Nonlinear

scholarly journals Existence of a renormalized solution of nonlinear parabolic equations with lower order term and general measure data

2021 ◽  
Vol 39 (3) ◽  
pp. 93-114
Author(s):  
A. Marah ◽  
Abdelkader Bouajaja ◽  
H. Redwane
Keyword(s):  
Lower Order ◽  
Parabolic Equations ◽  
Order Term ◽  
Nonlinear Parabolic Equations ◽  
Lower Order Term ◽  
Measure Data ◽  
General Measure ◽  
Renormalized Solution ◽  
Nonlinear Parabolic ◽  
The Right

We give an existence result of a renormalized solution for a classof nonlinear parabolic equations@b(u)/@t div(a(x; t;grad(u))+ H(x; t;ru) = ,where the right side is a general measure, b is a strictly increasing C1-function,div(a(x; t;grad(u)) is a Leray{Lions type operator with growth  in grad(u)and H(x; t;grad(u) is a nonlinear lower order term which satisfy the growth condition with respect to grad(u).

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.

Intrinsic scaling method for doubly nonlinear parabolic equations and its application

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Masashi Misawa ◽  
Kenta Nakamura
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Large Data ◽  
Nonlinear Parabolic Equations ◽  
Sobolev Type ◽  
Scaling Method ◽  
Nonlinear Parabolic ◽  
Doubly Nonlinear ◽  
Doubly Nonlinear Equation ◽  
Doubly Nonlinear Parabolic Equation

Abstract In this article, we consider a fast diffusive type doubly nonlinear parabolic equation, called 𝑝-Sobolev type flows, and devise a new intrinsic scaling method to transform the prototype doubly nonlinear equation to the 𝑝-Sobolev type flows. As an application, we show the global existence and regularity for the 𝑝-Sobolev type flows with large data.

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