The Local Strong and Weak Solutions for a Generalized Pseudoparabolic Equation

Abstract EN

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 C([0,T);Hs(R))⋂C1([0,T);Hs-1(R)) with s>3/2, while the existence of local weak solutions is proved in the space Hs(R) with 1≤s≤3/2.

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 C([0,∞);Hs(R))⋂C1([0,∞);Hs-1(R)) with s≥2.