Blow-Up Of Solutions To Problems For Nonlinear Hyperbolic Equation

ABSTRACT

Different physical phenomena can be represented in terms of nonlinear problems for partial differential equations, however such problems are often subjected to singularities. Thus it gives rise to a permanent research interest to such problems. In the present study we provide reviews of essential approach applied to Cauchy problems and initial-boundary problems for hyperbolic equations based on latest results in this field. Also in this research we investigate the following problem    utt +ut −uxx = F(u), u(x,0) = x 3 , ut(x,0) = g(x). Where we prove the existence of unique solution (u) of the problem for 0 < t < φ, which blows up to +∞ as t → φ.