ﻻ يوجد ملخص باللغة العربية
This paper is devoted to discussing the existence and uniqueness of weak solutions to time-fractional elliptic equations having time-dependent variable coefficients. To obtain the main result, our strategy is to combine the Galerkin method, a basic inequality for the fractional derivative of convex Lyapunov candidate functions, the Yoshida approximation sequence and the weak compactness argument.
We prove uniqueness for weak solutions to abstract parabolic equations with the fractional Marchaud or Caputo time derivative. We consider weak solutions in time for divergence form equations when the fractional derivative is transferred to the test function.
We examine the short and long-time behaviors of time-fractional diffusion equations with variable space-dependent order. More precisely, we describe the time-evolution of the solution to these equations as the time parameter goes either to zero or to infinity.
We investigate diffusion equations with time-fractional derivatives of space-dependent variable order. We examine the well-posedness issue and prove that the space-dependent variable order coefficient is uniquely determined among other coefficients o
This work is the second of the series of three papers devoted to the study of asymptotic dynamics in the chemotaxis system with space and time dependent logistic source,$$partial_tu=Delta u-chi ablacdot(u abla v)+u(a(x,t)-ub(x,t)),quad 0=Delta v-lamb
We consider Dirichlet problems for linear elliptic equations of second order in divergence form on a bounded or exterior smooth domain $Omega$ in $mathbb{R}^n$, $n ge 3$, with drifts $mathbf{b}$ in the critical weak $L^n$-space $L^{n,infty}(Omega ; m