scholarly journals A comment on the jäger-kačur linearization scheme for strongly nonlinear parabolic equations

1999 ◽  
Vol 44 (6) ◽  
pp. 481-496 ◽  
Author(s):  
Jiří Vala
Keyword(s):  
Parabolic Equations ◽  
Nonlinear Parabolic Equations ◽  
Strongly Nonlinear ◽  
Nonlinear Parabolic

Existence of renormalized solutions for strongly nonlinear parabolic problems with measure data

2016 ◽  
Vol 23 (3) ◽  
pp. 303-321 ◽  
Author(s):  
Youssef Akdim ◽  
Abdelmoujib Benkirane ◽  
Mostafa El Moumni ◽  
Hicham Redwane
Keyword(s):  
Growth Condition ◽  
Parabolic Equations ◽  
Nonlinear Parabolic Equations ◽  
Parabolic Problems ◽  
Measure Data ◽  
Renormalized Solution ◽  
Unbounded Function ◽  
Strongly Nonlinear ◽  
Nonlinear Parabolic ◽  
The Right

AbstractWe study the existence result of a renormalized solution for a class of nonlinear parabolic equations of the form${\partial b(x,u)\over\partial t}-\operatorname{div}(a(x,t,u,\nabla u))+g(x,t,u% ,\nabla u)+H(x,t,\nabla u)=\mu\quad\text{in }\Omega\times(0,T),$where the right-hand side belongs to ${L^{1}(Q_{T})+L^{p^{\prime}}(0,T;W^{-1,p^{\prime}}(\Omega))}$ and ${b(x,u)}$ is unbounded function of u, ${{-}\operatorname{div}(a(x,t,u,\nabla u))}$ is a Leray–Lions type operator with growth ${|\nabla u|^{p-1}}$ in ${\nabla u}$. The critical growth condition on g is with respect to ${\nabla u}$ and there is no growth condition with respect to u, while the function ${H(x,t,\nabla u)}$ grows as ${|\nabla u|^{p-1}}$.

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.

Kinetics of oxidation of ammonia on cobalt catalyst I model of the reactor with catalytically active wall

1982 ◽  
Vol 47 (8) ◽  
pp. 2087-2096 ◽  
Author(s):  
Bohumil Bernauer ◽  
Antonín Šimeček ◽  
Jan Vosolsobě
Keyword(s):  
Parabolic Equations ◽  
Cobalt Catalyst ◽  
Nonlinear Parabolic Equations ◽  
Catalytic Reactions ◽  
Temperature Profiles ◽  
Dimensional Model ◽  
Kinetics Of Oxidation ◽  
Nonlinear Parabolic ◽  
Catalytically Active ◽  
Kinetics Of

A two dimensional model of a tabular reactor with the catalytically active wall has been proposed in which several exothermic catalytic reactions take place. The derived dimensionless equations enable evaluation of concentration and temperature profiles on the surface of the active component. The resulting nonlinear parabolic equations have been solved by the method of orthogonal collocations.

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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