A nonlinear partial differential system arising in thermoelectricity

2005 ◽  
Vol 16 (6) ◽  
pp. 683-712 ◽  
Author(s):  
A. BERMÚDEZ ◽  
R. MUÑOZ-SOLA ◽  
F. PENA
Keyword(s):  
Source Term ◽  
A Priori Estimates ◽  
A Priori ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Existence Of A Solution ◽  
Nonlinear Parabolic ◽  
Priori Estimates ◽  
Partial Differential System ◽  
Temperature Equation

In this paper we prove the existence of a solution for a system of nonlinear parabolic partial differential equations arising from thermoelectric modelling of metallurgical electrodes undergoing a phase change. The model consists of an electromagnetic problem for eddy current computation coupled with a Stefan problem for temperature. The proof uses a regularized problem obtained by truncating the source term in temperature equation. Passing to the limit requires fine a priori estimates leading to compactness.

LIFESPAN ESTIMATES FOR SOLUTIONS OF POLYHARMONIC KIRCHHOFF SYSTEMS

2012 ◽  
Vol 22 (02) ◽  
pp. 1150009 ◽  
Author(s):  
GIUSEPPINA AUTUORI ◽  
FRANCESCA COLASUONNO ◽  
PATRIZIA PUCCI
Keyword(s):  
A Priori Estimates ◽  
Driving Forces ◽  
A Priori ◽  
Thin Plates ◽  
Existence Of A Solution ◽  
Dissipative Term ◽  
Maximal Solutions ◽  
Elastic Bodies ◽  
Priori Estimates ◽  
Deformation Processes

In mathematical physics we increasingly encounter PDEs models connected with vibration problems for elastic bodies and deformation processes, as it happens in the Kirchhoff–Love theory for thin plates subjected to forces and moments. Recently Monneanu proved in Refs. 26 and 27 the existence of a solution of the nonlinear Kirchhoff–Love plate model. In this paper we treat several questions about non-continuation for maximal solutions of polyharmonic Kirchhoff systems, governed by time-dependent nonlinear dissipative and driving forces. In particular, we are interested in the strongly damped Kirchhoff–Love model, containing also an intrinsic dissipative term of Kelvin–Voigt type. Global non-existence and a priori estimates for the lifespan of maximal solutions are proved. Several applications are also presented in special subcases of the source term f and the nonlinear external damping Q.

Estimates for a beam-like partial differential operator and applications

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Meriem Belahdji ◽  
Setti Ayad ◽  
Mohammed Hichem Mortad
Keyword(s):  
Differential Operator ◽  
A Priori Estimates ◽  
A Priori ◽  
Partial Differential Operator ◽  
Partial Differential ◽  
Priori Estimates

Abstract The aim of this paper is to provide some a priori estimates for a beam-like operator. Some applications and counterexamples are also given.

scholarly journals On a regularity property and a priori estimates for solutions of nonlinear parabolic variational inequalities

2000 ◽  
Vol 160 ◽  
pp. 123-134 ◽  
Author(s):  
Haruo Nagase
Keyword(s):  
Continuous Dependence ◽  
A Priori Estimates ◽  
Lower Semicontinuous ◽  
A Priori ◽  
Regularity Property ◽  
Regularity Properties ◽  
Nonlinear Parabolic ◽  
Priori Estimates ◽  
Lower Semicontinuous Functional ◽  
Continuous Dependence Of Solutions

AbstractIn this paper we consider the following nonlinear parabolic variational inequality; u(t) ∈ D(Φ) for all where Δp is the so-called p-Laplace operator and Φ is a proper, lower semicontinuous functional. We have obtained two results concerning to solutions of this problem. Firstly, we prove a few regularity properties of solutions. Secondly, we show the continuous dependence of solutions on given data u0 and f.

scholarly journals EIGENELEMENTS OF A GENERAL AGGREGATION-FRAGMENTATION MODEL

2010 ◽  
Vol 20 (05) ◽  
pp. 757-783 ◽  
Author(s):  
MARIE DOUMIC JAUFFRET ◽  
PIERRE GABRIEL
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
Asymptotic Behavior Of Solutions ◽  
Fragmentation Model ◽  
Existence Of A Solution ◽  
Priori Estimates ◽  
Long Time ◽  
Weighted Norms ◽  
Fragmentation Processes ◽  
Time Asymptotic Behavior

We consider a linear integro-differential equation which arises to describe both aggregation-fragmentation processes and cell division. We prove the existence of a solution (λ, [Formula: see text], ϕ) to the related eigenproblem. Such eigenelements are useful to study the long-time asymptotic behavior of solutions as well as the steady states when the equation is coupled with an ODE. Our study concerns a non-constant transport term that can vanish at x = 0, since it seems to be relevant to describe some biological processes like proteins aggregation. Non-lower-bounded transport terms bring difficulties to find a priori estimates. All the work of this paper is to solve this problem using weighted-norms.

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