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Consistent models for electrical networks with distributed parameters

Corneliu A. Marinov, Gheorghe Moroşanu (1992)

Mathematica Bohemica

A system of one-dimensional linear parabolic equations coupled by boundary conditions which include additional state variables, is considered. This system describes an electric circuit with distributed parameter lines and lumped capacitors all connected through a resistive multiport. By using the monotony in a space of the form $L^{2} (0, T; H^{1})$ , one proves the existence and uniqueness of a variational solution, if reasonable engineering hypotheses are fulfilled.

Continuability in time of smooth solutions of strong-nonlinear nondiagonal parabolic systems

Arina Arkhipova (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

A class of quasilinear parabolic systems with quadratic nonlinearities in the gradient is considered. It is assumed that the elliptic operator of a system has variational structure. In the multidimensional case, the behavior of solutions of the Cauchy-Dirichlet problem smooth on a time interval $[0, T)$ is studied. Smooth extendibility of the solution up to $t = T$ is proved, provided that “normilized local energies” of the solution are uniformly bounded on $[0, T)$ . For the case where $[0, T)$ determines the maximal interval...

Coupling the Stokes and Navier–Stokes equations with two scalar nonlinear parabolic equations

Macarena Gómez Mármol, Francisco Ortegón Gallego (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This work deals with a system of nonlinear parabolic equations arising in turbulence modelling. The unknowns are the N components of the velocity field u coupled with two scalar quantities θ and φ. The system presents nonlinear turbulent viscosity $A (θ, ϕ)$ and nonlinear source terms of the form $θ^{2} {| \nabla u |}^{2}$ and ${θ ϕ | \nabla u |}^{2}$ lying in L1. Some existence results are shown in this paper, including $L^{\infty}$ -estimates and positivity for both θ and φ.

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