scholarly journals Periodic solutions to nonlinear parabolic differential equations

1977 ◽  
Vol 7 (2) ◽  
pp. 297-312 ◽  
Author(s):  
Robert Gaines ◽  
Wolfgang Walter
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Parabolic Differential Equations ◽  
Nonlinear Parabolic

scholarly journals Periodic solutions of certain nonlinear parabolic differential equations in domains with periodically moving boundaries

1978 ◽  
Vol 70 ◽  
pp. 111-123 ◽  
Author(s):  
Yoshio Yamada
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Moving Boundaries ◽  
Typical Problem ◽  
Parabolic Differential Equations ◽  
Periodic Problems ◽  
Nonlinear Parabolic

In this paper we consider the periodic problems for certain nonlinear parabolic differential equations in domains with periodically moving boundaries. The typical problem, which is going to be discussed in the present paper, is to solve the following:

scholarly journals On Some regularity properties for solutions of nonlinear parabolic differential equations

1992 ◽  
Vol 128 ◽  
pp. 49-63 ◽  
Author(s):  
Haruo Nagase
Keyword(s):  
Differential Equations ◽  
Bounded Domain ◽  
Open Interval ◽  
Function Spaces ◽  
Parabolic Differential Equations ◽  
Regularity Properties ◽  
Nonlinear Parabolic ◽  
Class C

Let G be a bounded domain in Rn with coordinates x = (x1,…,xn) and let its boundary S be of class C2. We assume that the usual function spaces Lq(G), Wl, q(G) and are known. We write the norm of Lq(G) by | |q and the adjoint number of q by q*, i.e., q* = q/(q —1).For any positive number T we denote the open interval (0,T) by I, the cylinder G X I in Rn+1 by Q and the norm of Lq(Q) by ‖ ‖q.

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