First boundary value problem for cordes-type semilinear parabolic equation with discontinuous coefficients
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CitationHarman, A., Harman, E. (2020). First boundary value problem for cordes-type semilinear parabolic equation with discontinuous coefficients. Journal of Mathematics. https://doi.org/10.1155/2020/1019038
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.
SourceJournal of Mathematics
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