Abstract
In this paper, we study the existence and uniqueness of the global generalized solution and strong solution of the initial-boundary value problem and the corresponding initial value problem for the nonlinear pseudoparabolic equation in arbitrary dimensions $$u_t - \Delta u_t = f\left( {x,t,u,\nabla u} \right) + \nabla \cdot \phi \left( {x,t,u,\nabla u} \right).$$ Besides, the smoothness, asymptotic behaviors and blow-up of the solutions are also discussed. The results not only include but also improve and generalize the main results concerning this class of equations.
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