scholarly journals An inverse problem for a system of nonlinear parabolic equations

2021 ◽  
Vol 2099 (1) ◽  
pp. 012047
Author(s):  
E Tabarintseva
Keyword(s):  
Inverse Problem ◽  
Approximate Solution ◽  
Error Estimate ◽  
Parabolic Equations ◽  
Regularization Method ◽  
Nonlinear Parabolic Equations ◽  
Distributed Model ◽  
Order Estimate ◽  
Optimal Method ◽  
Nonlinear Parabolic

Abstract The inverse problem for a system of nonlinear parabolic equations is considered in the present paper. Namely, it is required to restore the initial condition by a given time-average value of the solution to the system of the nonlinear parabolic equations. An exact in the order error estimate of the optimal method for solving the inverse problem through the error estimate for the corresponding linear problem is obtained. A stable approximate solution to the unstable nonlinear problem under study is constructed by means of the projection regularization method which consists of using the representation of the approximate solution as a partial sum of the Fourier series. An exact in the order estimate for the error of the projection regularization method is obtained on one of the standard correctness classes. As a consequence, it is proved the optimality of the projection regularization method. As an example of a nonlinear system of parabolic equations, which has important practical applications, a spatially distributed model of blood coagulation is considered.

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.

Quasilinearization Methods for Nonlinear Parabolic Equations with Functional Dependence

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.

scholarly journals Diffuse measures and nonlinear parabolic equations

2011 ◽  
Vol 11 (4) ◽  
pp. 861-905 ◽  
Author(s):  
Francesco Petitta ◽  
Augusto C. Ponce ◽  
Alessio Porretta
Keyword(s):  
Parabolic Equations ◽  
Nonlinear Parabolic Equations ◽  
Nonlinear Parabolic
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