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Blow-up phenomena for nonlinear pseudo-parabolic equations with gradient term
Università di Cagliari, Dipartimento di Matematica e Informatica, V.le Merello 92,09123 Cagliari, Italy |
$\left\{ \begin{array}{l}\begin{split}u_t- \lambda \triangle u_t=& k(t) \text{div}(g(| \nabla u|^2) \nabla u) +f(t,u,| \nabla u| ) \quad {\rm in} \ \Omega \times (0, t^*), \\[6pt] u=&0 \ \qquad {\rm on} \ \partial \Omega \times (0,t^*),\\[6pt] u ({ x},0) =& u_0 ({ x}) \quad {\rm in} \ \Omega,\\[6pt]\end{split}\end{array} \right.$ |
$\Omega$ |
$\mathbb{R}^n, \ n\geq 2$ |
$ \partial \Omega$ |
$ k$ |
$t$ |
$u(x,t)$ |
$t^*$ |
$[0,t^*)$ |
$u(x,t).$ |
References:
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References:
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