A priori estimates for a solution to the first initial-boundary-value problem for a system of fully nonlinear parabolic equations

1999 ◽  
Vol 97 (4) ◽  
pp. 4206-4224
Author(s):  
Ya. I. Belopol'skaya
Keyword(s):  
Boundary Value Problem ◽  
Parabolic Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Parabolic Equations ◽  
Nonlinear Parabolic ◽  
Priori Estimates ◽  
Initial Boundary Value

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.

On the Dynamic Contact Problem for a Viscoelastic Plate

2010 ◽  
Author(s):  
Igor Bock
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Dynamic Contact ◽  
Viscoelastic Plate ◽  
Weak Formulation ◽  
Priori Estimates ◽  
Elliptic Variational Inequalities ◽  
Initial Boundary Value

We deal with an initial-boundary value problem describing the perpendicular vibrations of an anisotropic viscoelastic plate free on its boundary and with a rigid inner obstacle. A weak formulation of the problem is in the form of the hyperbolic variational inequality. We solve the problem using the discretizing the time variable. The elliptic variational inequalities for every time level are uniquely solved. We derive the a priori estimates and the convergence of the sequence of segment line functions to a variational solution of the considered problem.

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