The Cauchy problem for a nonlinear generalized pseudoparabolic equation is investigated. The well-posedness of local strong solutions for the problem is established in the Sobolev space with , while the existence of local weak solutions is proved in the space with . Further, under certain assumptions of the nonlinear terms in the equation, it is shown that there exists a unique global strong solution to the problem in the space with .
"The Local Strong and Weak Solutions for a Generalized Pseudoparabolic Equation." Abstr. Appl. Anal. 2012 (SI11) 1 - 12, 2012. https://doi.org/10.1155/2012/568404