Equations of parabolic type in a Banach space

1966 ◽  
pp. 1-62 ◽  
Author(s):  
P. E. Sobolevskiĭ
Keyword(s):  
Banach Space ◽  
Parabolic Type

scholarly journals A Note on the Stability of the Integral-Differential Equation of the Parabolic Type in a Banach Space

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Maksat Ashyraliyev
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Difference Scheme ◽  
Unique Solvability ◽  
Parabolic Type ◽  
Stability Estimates ◽  
The Difference ◽  
The Stability ◽  
Integral Differential Equation

The integral-differential equation of the parabolic type in a Banach space is considered. The unique solvability of this equation is established. The stability estimates for the solution of this equation are obtained. The difference scheme approximately solving this equation is presented. The stability estimates for the solution of this difference scheme are obtained.

scholarly journals The fundamental solutions for fractional evolution equations of parabolic type

2004 ◽  
Vol 2004 (3) ◽  
pp. 197-211 ◽  
Author(s):  
Mahmoud M. El-Borai
Keyword(s):  
Banach Space ◽  
Continuous Dependence ◽  
Evolution Equations ◽  
Initial Conditions ◽  
Parabolic Type ◽  
Fundamental Solutions ◽  
Parabolic Partial Differential Equations ◽  
Fractional Evolution Equations ◽  
Closed Operators ◽  
Continuous Dependence Of Solutions

The fundamental solutions for linear fractional evolution equations are obtained. The coefficients of these equations are a family of linear closed operators in the Banach space. Also, the continuous dependence of solutions on the initial conditions is studied. A mixed problem of general parabolic partial differential equations with fractional order is given as an application.

scholarly journals Existence and decay of solutions of some nonlinear parabolic variational inequalities

1980 ◽  
Vol 3 (1) ◽  
pp. 79-102 ◽  
Author(s):  
Mitsuhiro Nakao ◽  
Takashi Narazaki
Keyword(s):  
Banach Space ◽  
Nonlinear Operator ◽  
Convex Set ◽  
Parabolic Type ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Nonlinear Parabolic ◽  
Decay Of Solutions ◽  
Monotonicity Assumption ◽  
Closed Convex Set

This paper discusses the existence and decay of solutionsu(t)of the variational inequality of parabolic type:<u′(t)+Au(t)+Bu(t)−f(t),   v(t)−u(t)>≧0for∀v∈Lp([0,∞);V)(p≧2)withv(t)∈Ka.e. in[0,∞), whereKis a closed convex set of a separable uniformly convex Banach spaceV,Ais a nonlinear monotone operator fromVtoV*andBis a nonlinear operator from Banach spaceWtoW*.VandWare related asV⊂W⊂Hfor a Hilbert spaceH. No monotonicity assumption is made onB.

SOME NON-DISSIPATIVITY CONDITION FOR EVOLUTION EQUATIONS

2013 ◽  
Vol 24 (02) ◽  
pp. 1350002
Author(s):  
CHIN-YUAN LIN
Keyword(s):  
Banach Space ◽  
Nonlinear Evolution Equation ◽  
Evolution Equations ◽  
Real Banach Space ◽  
Nonlinear Evolution ◽  
Parabolic Type ◽  
Time Dependent ◽  
Linear Partial Differential Equations ◽  
Time Dependent Domain ◽  
Dependent Domain

Of concern is the nonlinear evolution equation [Formula: see text] in a real Banach space X, where the nonlinear, time-dependent, multi-valued operator [Formula: see text] has a time-dependent domain D(A(t)). It will be shown that, under some non-dissipativity condition, the equation has a strong solution. Illustrations are given of solving quasi-linear partial differential equations of parabolic type.

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