Stable Structures of Nonlinear Parabolic Equations with Transformation of Spatial Variables

In this paper, we consider solutions of nonlinear parabolic equations in the half-space.It is well-known that, in the case of linear equations, one needs to impose additional conditions on solutions for the validity of the maximum principle. The most famous of them are the conditions of Tikhonov and T¨acklind. We show that such restrictions are not needed for a wide class of nonlinear equations. In so doing, the coeﬃcients of lower-order derivatives can grow arbitrarily as the spatial variables tend to inﬁnity.We give an example which demonstrates an application of the obtained re- sults for nonlinearities of the Emden - Fowler type.

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

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19822087 ◽

1982 ◽

Vol 47 (8) ◽

pp. 2087-2096 ◽

Cited By ~ 3

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.

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

Calculus of Variations and Partial Differential Equations ◽

10.1007/s00526-021-02044-z ◽

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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Entropy Solutions for Nonlinear Parabolic Equations with Nonstandard Growth in Non-reflexive Orlicz Spaces

Mediterranean Journal of Mathematics ◽

10.1007/s00009-020-01668-3 ◽

2021 ◽

Vol 18 (1) ◽

Author(s):

M. Bourahma ◽

A. Benkirane ◽

J. Bennouna

Keyword(s):

Parabolic Equations ◽

Orlicz Spaces ◽

Nonlinear Parabolic Equations ◽

Entropy Solutions ◽

Nonstandard Growth ◽

Nonlinear Parabolic

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Quasilinearization Methods for Nonlinear Parabolic Equations with Functional Dependence

Georgian Mathematical Journal ◽

10.1515/gmj.2002.431 ◽

2002 ◽

Vol 9 (3) ◽

pp. 431-448

Author(s):

A. Bychowska

Keyword(s):

Cauchy Problem ◽

Parabolic Equations ◽

Unknown Function ◽

Functional Dependence ◽

Nonlinear Parabolic Equations ◽

Quasilinearization Method ◽

Convergence Theorems ◽

Nonlinear Parabolic ◽

Quasilinearization Methods ◽

Derivatives Of

Abstract We consider a Cauchy problem for nonlinear parabolic equations with functional dependence. We prove convergence theorems for a general quasilinearization method in two cases: (i) the Hale functional acting only on the unknown function, (ii) including partial derivatives of the unknown function.

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