We study the initial value problem for the nonlinear dissipative equations (Formula presented.) where a ∈ R n , ρ > 1, σ > 0. We prove that if (Formula presented.) and (Formula presented.) then in the case σ = (ρ − 1)/(n + 1) solutions exist globally and decay as (Formula presented.) And in the case 0 < σ < (ρ − 1)/(n + 1), σ is close to (ρ − 1)/(n + 1), solutions have estimates (Formula presented.).
- 1991 Mathematics Subject Classifications: Primary 35Q35
- Burgers type equation
- Dissipative nonlinear evolution equation
- Large time asymptotics
ASJC Scopus subject areas
- Environmental Chemistry
- Plant Science