Abstract
For a class of semilinear parabolic equations with discontinuous coefficients, the strong solvability of the Dirichlet problem is studied in this paper. The problem ∑i,j=1naijt,xuxixj−ut+gt,x,u=ft,x,uΓQT=0, in QT=Ω×0,T is the subject of our study, where Ω is bounded C2 or a convex subdomain of En+1,ΓQT=∂QT\∖t=T. The function gx,u is assumed to be a Caratheodory function satisfying the growth condition gt,x,u≤b0uq, for b0>0,q∈0,n+1/n−1,n≥2, and leading coefficients satisfy Cordes condition b0>0,q∈0,n+1/n−1,n≥2.
Highlights
Let En be an n-dimensional Euclidean space of points x (x1, x2, . . . , xn) and Ω be a bounded domain in En with boundary zΩ of the class C2 or a convex domain
For a class of semilinear parabolic equations with discontinuous coefficients, the strong solvability of the Dirichlet problem is studied in our study, this paper. where Ω is bouenpdreodblCem2 or ani,jc o1 navije(xt,sxu)budxoixmj −aiunto+f g(t, x, u) En+1, Γ(QT)
For the strong solvability problem in W_ 2p(Ω) for any p > 1 for parabolic equations with discontinuous coefficients, we refer [8, 14, 15], where the leading coefficients are taken from the VMO class
Summary
For a class of semilinear parabolic equations with discontinuous coefficients, the strong solvability of the Dirichlet problem is studied in our study, this paper. Where Ω is bouenpdreodblCem or ani,jc o1 navije(xt,sxu)budxoixmj −aiunto+f g(t, x, u) En+1, Γ(QT). 0, in QT Ω × (0, T) e function g(x, u) is is the subject of assumed to be a Caratheodory function satisfying the growth condition |g(t, x, u)| ≤ b0|u|q, for b0 > 0, q ∈ (0, (n + 1)/(n − 1)), n ≥ 2, and leading coefficients satisfy Cordes condition b0 > 0, q ∈ (0, (n + 1)/(n − 1)), n ≥ 2
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
