BLOW-UP AND NONGLOBAL SOLUTION FOR A FAMILY OF NONLINEAR HIGHER-ORDER EVOLUTION PROBLEM

ABSTRACT. In this paper we consider a kind of higher-order evolution equation asku ¶tk + ¶k−1u ¶tk−1 +···+ut −4u= f (u,5u,x). For this equation, we investigate nonglobal solution, blow-up in finite time and instantaneous blow-up under some assumption on k, f and initial data. In this paper we employ the Test function method, the Generalized convexity method and Galerkin’s method for some of our proofs. Moreover, occasionally by changing P.D.E problems to some ordinary differential inequalities, we investigate this kind of higher-order evolution equations.