[HTML][HTML] Global existence of solutions to a nonlinear anomalous diffusion system
… In this paper, we consider the following system of nonlinear fractional in space reaction–diffusion
equations (1.1) { u t ( x , t ) + t a ( − Δ ) α u ( x , t ) = A ( t ) v r ( x , t ) u s ( x , t ) , x ∈ R N , t > 0 ,
v t ( x , t ) + t b ( − Δ ) β v ( x , t ) = B ( t ) v p ( x , t ) u q ( x , t ) , x ∈ R N , t > 0 , for u > 0 , v > 0 ,
equipped with the initial conditions (1.2) u ( x , 0 ) = u 0 ( x ) , v ( x , 0 ) = v 0 ( x ) , x ∈ R N ,
where the initial data u 0 , v 0 ∈ C L B ( R N ) ≔ { ϕ ∈ C ( R N ) : ϕ ≥ c > 0 } , are given
functions, a > 0 , b > 0 , s < 0 , p < 0 , r < 1 − p and q < 1 − s . The functions A and B are such�…
equations (1.1) { u t ( x , t ) + t a ( − Δ ) α u ( x , t ) = A ( t ) v r ( x , t ) u s ( x , t ) , x ∈ R N , t > 0 ,
v t ( x , t ) + t b ( − Δ ) β v ( x , t ) = B ( t ) v p ( x , t ) u q ( x , t ) , x ∈ R N , t > 0 , for u > 0 , v > 0 ,
equipped with the initial conditions (1.2) u ( x , 0 ) = u 0 ( x ) , v ( x , 0 ) = v 0 ( x ) , x ∈ R N ,
where the initial data u 0 , v 0 ∈ C L B ( R N ) ≔ { ϕ ∈ C ( R N ) : ϕ ≥ c > 0 } , are given
functions, a > 0 , b > 0 , s < 0 , p < 0 , r < 1 − p and q < 1 − s . The functions A and B are such�…
Abstract
A nonlinear system with different anomalous diffusion terms is considered. The existence of global positive solutions is proved.
Elsevier
Showing the best result for this search. See all results