Strict solution of a nonlinear evolution problem in a time dependent domain

1980 ◽  
Vol 4 (6) ◽  
pp. 1135-1149
Author(s):  
Giovanni Borgioli ◽  
Giorgio Busoni ◽  
Giovanni Frosali
Keyword(s):  
Nonlinear Evolution ◽  
Time Dependent ◽  
Evolution Problem ◽  
Strict Solution ◽  
Time Dependent Domain ◽  
Nonlinear Evolution Problem ◽  
Dependent Domain

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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