Abstract
The initial boundary value problem for a nonlinear hyperbolic equation with Lewis function in a bounded domain is considered. In this work, the main result is that the solution blows up in finite time if the initial data possesses suitable positive energy. Moreover, the estimates of the lifespan of solutions are also given.
Highlights
Let Ω be a bounded domain in Rn with smooth boundary ∂Ω
Zhou 10 considered the initial boundary value problem for a quasilinear parabolic equation with a generalized Lewis function which depends on both spacial variable and time. He obtained the blowup of solutions with positive initial energy
Let t0 be a number that depends on p, E0 − E 0, ∇u0 L2 Ω, and μ x as t0 >
Summary
Received 17 February 2009; Accepted 28 September 2009 Recommended by Gary Lieberman The initial boundary value problem for a nonlinear hyperbolic equation with Lewis function in a bounded domain is considered. The main result is that the solution blows up in finite time if the initial data possesses suitable positive energy. The estimates of the lifespan of solutions are given.
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