scholarly journals Global Lipschitz regularizing effects for linear and nonlinear parabolic equations

2013 ◽  
Vol 100 (5) ◽  
pp. 633-686 ◽  
Author(s):  
A. Porretta ◽  
E. Priola
Keyword(s):  
Parabolic Equations ◽  
Nonlinear Parabolic Equations ◽  
Nonlinear Parabolic ◽  
Linear And Nonlinear ◽  
Regularizing Effects

Prescribed conditions at infinity for parabolic equations

2014 ◽  
Vol 17 (01) ◽  
pp. 1450004 ◽  
Author(s):  
Shoshana Kamin ◽  
Fabio Punzo
Keyword(s):  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Nonlinear Parabolic Equations ◽  
Time Dependent ◽  
Bounded Solutions ◽  
Nonlinear Parabolic ◽  
Linear And Nonlinear ◽  
Conditions At Infinity

We are concerned with existence and uniqueness of the solutions for linear and nonlinear parabolic equations with time-dependent coefficients, in the class of bounded solutions satisfying appropriate conditions at infinity.

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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