Uzay değişkenine bağlı sönüm terimli yarılineer dalga denklemi için kritik üs

The thesis is a survey concerning with the global existence and blow-up of solutions of the Cauchy problem for the semilinear damped wave equations utt 􀀀 u + V(x)ut = jujp; x 2 Rn; t > 0; u(x; 0) = "u0(x); ut(x; 0) = "u1(x); x 2 Rn; where 1 < p < n+2 n􀀀2 is a real number, " > 0 is a small number and V(x) is the potential or the friction term like V(x) s V0(1 + jxj)􀀀 for large jxj, where V0 > 0 and 2 [0; 1) are constants. The number pc = 1 + 2 n􀀀 is the critical value of p in the sense that if 1 < p pc, then solutions blow-up in finite time; if pc < p < n+2 n􀀀2 , then there exist small data global solutions. Keywords: semilinear damped wave equation, space dependent damping, global solution, blow up of the solution, decay rate of the energy.