The method of lines for nonlinear parabolic differential equations with mixed derivatives

1979 ◽  
Vol 32 (2) ◽  
pp. 197-207 ◽  
Author(s):  
Alexander Voigt
Keyword(s):  
Differential Equations ◽  
Method Of Lines ◽  
Parabolic Differential Equations ◽  
Nonlinear Parabolic ◽  
The Method Of Lines ◽  
Mixed Derivatives

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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