Mixed initial boundary-value problems for semi-linear parabolic equations

1967 ◽  
Vol 34 (3) ◽  
pp. 481-491 ◽  
Author(s):  
Bui An Ton
Keyword(s):  
Boundary Value Problems ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Linear Parabolic Equations ◽  
Initial Boundary Value

On nonclassical problems for first-order evolution equations

2011 ◽  
Vol 18 (3) ◽  
pp. 441-463
Author(s):  
Gia Avalishvili ◽  
Mariam Avalishvili
Keyword(s):  
Boundary Value Problems ◽  
Parabolic Equations ◽  
Evolution Equations ◽  
Initial Conditions ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
First Order ◽  
Uniqueness Results ◽  
Initial Boundary Value

Abstract The present paper deals with nonclassical initial-boundary value problems for parabolic equations and systems and their generalizations in abstract spaces. Nonclassical problems with nonlocal initial conditions for an abstract first-order evolution equation with time-dependent operator are considered, the existence and uniqueness results are proved and the algorithm of approximation of nonlocal problems by a sequence of classical problems is constructed. Applications of the obtained general results to initial-boundary value problems for parabolic equations and systems are considered.

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