Solvability and maximal regularity results for a differential equation with diffusion coefficient

Authors : Kordan Ospanov, Adılet Yesbayev

Pages : 1304-1316

Doi:10.3906/mat-2002-87

View : 12 | Download : 0

Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :We consider a second-order differential equation with rapidly growing intermediate coefficients. We obtain a solvability result in the cases that the diffusion coefficient of equation is unbounded or it tends to zero at the infinity. Under additional conditions, we prove the $L_p - $ maximal regularity estimate for the solution of this equation.
Keywords : Second-order differential equation, unbounded intermediate coefficient, existence of a solution, uniqueness, maximal regularity estimate