Local regularity, boundary values and maximum principles for pseudoparabolic equations

Abstract

The regularity or singularity uf data at a point is shown to be preserved for all time at that point along the solution of a pseudoparabolic equation. This significantly strengthens earlier results on the perseverance of global regularity of data and furthermore shows that any local singularities in initial data are stationary, These results yxeld a precise description of the boundary values of a solution and explain certain non-standard maximum principles for pseudoparabolic equations

AMS(MOS)Classification Numbers:

• 35K70
• 35B05
• 35B30
• 35B65