Well-posedness of the solution of the fractional semilinear pseudo-parabolic equation

Abstract

Abstract This article concerns the Cauchy problem for the fractional semilinear pseudo-parabolic equation. Through the Green’s function method, we prove the pointwise convergence rate of the solution. Furthermore, using this precise pointwise structure, we introduce a Sobolev space condition with negative index on the initial data and give the nonlinear critical index for blowing up.

Keywords

• Fractional semilinear pseudo-parabolic equation
• Green’s function method
• Pointwise
• Negative index