Blow-up of solutions for a class of nonlinear pseudoparabolic equations with a memory term
Summary: We consider the nonlinear pseudoparabolic equation with a memory term \(u_t - \Delta u - \Delta u_t + \int_0^t \lambda \left(t - \tau\right) \Delta u \left(\tau\right) d \tau = \text{d} \text{i} \text{v} \left(\left|\nabla u\right|^{p - 2} u\right) + u^{1 + \alpha}\), \(x \in \Omega\), \(t > 0\), with an initial condition and Dirichlet boundary condition. Under negative initial energy and suitable conditions on \(p\), \(\alpha\), and the relaxation function \(\lambda(t)\), we prove a finite-time blow-up result by using the concavity method.
scientific article; zbMATH DE number 7022510
scientific article