<p style='text-indent:20px;'>We study the well-posedness of a semi-linear fractional diffusion equation and formulate an associated inverse problem. We determine power type nonlinearities from exterior partial measurements Dirichlet-to-Neumann map. Our arguments are based on first order linearization as well parabolic Runge approximation property.</p>

We study the inverse problem of recovering source function in a degenerate parabolic equation with many spatial variables. An additional integral observation condition is imposed. find sufficient conditions for unique solvability cases where unknown looked space L2(0, T) or L∞(0, T). The results obtained are based on preliminary corresponding direct which independent interest.

in this paper we consider a petrovsky viscoelastic inverse source problem with memory term in the boundary condition. we obtain sufficient conditions on relaxation function and initial data for which the solutions of problem are asymptotically stable when the integral overdetermination tends to zero as time goes to infinity.

‎in this study‎, ‎properties of spectral characteristic are investigated for‎ ‎singular sturm-liouville operators in the case where an eigen‎ ‎parameter not only appears in the differential equation but is‎ ‎also linearly contained in the jump conditions‎. ‎also weyl function‎ ‎for considering operator has been defined and the theorems which‎ ‎related to uniqueness of solution of inverse proble...

mathematical simulation of flow toward drains is an important and indispensable stage in drainage design and management. many related models have been developed, but most of them simulate the saturated flow toward drains without a due consideration of the unsaturated zone. in this study, the two dimensional differential equation governing saturated and unsaturated flow in porous media is numeri...

in this paper, two inverse problems of stephen kind with local (dirichlet) boundary conditions are investigated. in the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. for the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and bounda...

We present a method of reconstructing the region of origin and trajectories for particles given impact directions and positions. This method works for nonlinear trajectories, such as parabolic motion or motion with drag if given drag parameters. Our method works if given the impact speeds as well, or they can be estimated using a similar total initial energy prior. We apply our algorithm to the...