B-evolutions and sobolev equations

Abstract

We apply the results on B-evolutions as developed by Sauer to the Sobolev equation ∂^t:(Mu)+Lu=0 with initial condition Mu∣_{t = 0} = y and homogeneous boundaryconditions. M and L are uniformly strongly elliptic differential operators. Results on admissible initial conditions for strong solutions are obtained and compared to those of Fichera and Showalter.

Keywords:

• Sobolev equations
• B-evolution
• semi-group
• initial value problem
• elliptic differential operator

AMS(MOS):

• 34G
• 35Q