Nonexistence of weak solutions for evolution problems on \(\mathbb R^n\). (English) Zbl 1071.35089

Hakem, Ali

Bull. Belg. Math. Soc. - Simon Stevin 12, No. 1, 73-82 (2005).

Summary: We study the nonexistence of global weak solutions for equations of the following type \[ u_{tt}-\Delta u+ g(t) u_t= |u|^p,\tag{1} \] where \(g(t)\) behaves like \(t^\beta\), \(0\leq\beta< 1\). Then the situation is extended to systems of equations of the same type, and more general equation than (1).
Editorial remark: The paper is identical to the letter with the author’s paper [Math. Nachr. 278, No. 9, 1033–1040 (2005; Zbl 1074.35074)].

MSC:

35L70	Second-order nonlinear hyperbolic equations
35B40	Asymptotic behavior of solutions to PDEs

Keywords:

global weak solutions

Citations:

Zbl 1074.35074