Convergent difference schemes for nonlinear parabolic equations and mean curvature motion

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.

Download Full-text

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.

Download Full-text

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

Download Full-text

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.

Download Full-text