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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
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