## Weak solutions for a viscous $$p$$-Laplacian equation.(English)Zbl 1036.35145

Summary: We consider the pseudoparabolic equation $$u_t-k\Delta u_t=\text{ div}(| \nabla u|^{p-2}\nabla u)$$. By using the time-discrete method, we establish the existence of weak solutions, and also discuss the uniqueness.

### MSC:

 35L70 Second-order nonlinear hyperbolic equations 35D05 Existence of generalized solutions of PDE (MSC2000) 35K55 Nonlinear parabolic equations
Full Text: