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.

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.

scholarly journals A Boundary Value Problem with Multivariables Integral Type Condition for Parabolic Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-13
Author(s):  
A. L. Marhoune ◽  
F. Lakhal
Keyword(s):  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Continuous Dependence ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Analysis Method ◽  
Type Condition ◽  
Integral Type ◽  
Priori Estimates

We study a boundary value problem with multivariables integral type condition for a class of parabolic equations. We prove the existence, uniqueness, and continuous dependence of the solution upon the data in the functional wieghted Sobolev spaces. Results are obtained by using a functional analysis method based on two-sided a priori estimates and on the density of the range of the linear operator generated by the considered problem.

scholarly journals Explicit Blowing Up Solutions for a Higher Order Parabolic Equation with Hessian Nonlinearity

2021 ◽  
Author(s):  
Carlos Escudero
Keyword(s):  
Blow Up ◽  
A Priori Estimates ◽  
A Priori ◽  
Higher Order ◽  
Order Partial Differential Equation ◽  
Infinite Time ◽  
Nonlinear Parabolic ◽  
Priori Estimates ◽  
Blowing Up ◽  
Blowing Up Solutions

AbstractIn this work we consider a nonlinear parabolic higher order partial differential equation that has been proposed as a model for epitaxial growth. This equation possesses both global-in-time solutions and solutions that blow up in finite time, for which this blow-up is mediated by its Hessian nonlinearity. Herein, we further analyze its blow-up behaviour by means of the construction of explicit solutions in the square, the disc, and the plane. Some of these solutions show complete blow-up in either finite or infinite time. Finally, we refine a blow-up criterium that was proved for this evolution equation. Still, existent blow-up criteria based on a priori estimates do not completely reflect the singular character of these explicit blowing up solutions.

XXII.—A Priori Estimates and Nonlinear Parabolic Equations of Arbitrary Order

1972 ◽  
Vol 69 (4) ◽  
pp. 287-293
Author(s):  
D. E. Edmunds ◽  
C. A. Stuart
Keyword(s):  
Parabolic Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Parabolic Equations ◽  
Linear Parabolic Equation ◽  
Nonlinear Parabolic ◽  
Priori Estimates ◽  
Initial Boundary Value

SynopsisIn this paper it is shown that the question of the existence of a classical solution of the first initial-boundary value problem for a non-linear parabolic equation may be reduced to the problem of the derivation of suitable a priori bounds.

scholarly journals On the solvability of a class of reaction-diffusion systems

2006 ◽  
Vol 2006 ◽  
pp. 1-15 ◽  
Author(s):  
Abdelfatah Bouziani ◽  
Ilham Mounir
Keyword(s):  
Iterative Process ◽  
Continuous Dependence ◽  
A Priori Estimates ◽  
A Priori ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Priori Estimates ◽  
Quasilinear Systems ◽  
Linearized Problem

We deal with a class of parabolic reaction-diffusion systems. We use an iterative process based on results obtained for a linearized problem, then we derive some a priori estimates to establish the existence, uniqueness, and continuous dependence of the weak solution for a class of quasilinear systems.

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