On a nonlinear parabolic equation involving Bessel's operator associated with a mixed inhomogeneous condition

AbstractIn this paper we consider the following nonlinear parabolic equation(*)ut-a(t)urr+γrur+F(r,u)=f(r,t),0<r<1,0<t<T,limr→0+rγ/2ur(r,t)<+∞,ur(1,t)+h(t)(u(1,t)-u˜0)=0,u(r,0)=u0(r),where γ>0, u˜0 are given constants, a(t), h(t), F(r,u), f(r,t) are given functions. In Section 3, we use the Galerkin and compactness method in appropriate Sobolev spaces with weight to prove the existence of a unique weak solution of the problem (*) on (0,T), for every T>0. In Section 4, we prove that if the initial condition is bounded, then so is the solution. In Section 5, we study asymptotic behavior of the solution as t→+∞. In Section 6 we give numerical results