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

Liu, Changchun

Electron. J. Differ. Equ. 2003, Paper No. 63, 11 p. (2003).

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

Keywords:

Pseudoparabolic equations; existence; uniqueness; time-discrete method