2 citations · 4 across the 4 of their papers we have counts for
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Higher order hypoelliptic damped wave equations on graded Lie groups with data from negative order Sobolev spaces: the critical case
Vishvesh Kumar, Shyam Swarup Mondal, Michael Ruzhansky +1
Let be a graded Lie group with homogeneous dimension . In this paper, we study the Cauchy problem for a semilinear hypoelliptic damped wave equation involving a posi…
Liouville theorems for Kirchhoff-type hypoelliptic Partial Differential Equations and systems. I. Heisenberg group
Aidyn Kassymov, Michael Ruzhansky, Niyaz Tokmagambetov +1
In this paper, we show the nonexistence results for the Kirchhoff elliptic, parabolic, and hyperbolic type equations on the Heisenberg groups. Also, the pseudo-parabolic and pseudo…
Global existence and blow-up for space and time nonlocal reaction-diffusion equation
Ahmed Alsaedi, Mokhtar Kirane, Berikbol T. Torebek
A time-space fractional reaction-diffusion equation in a bounded domain is considered. Under some conditions on the initial data, we show that solutions may experience blow-up in a…
Inverse source problems for positive operators. I. Hypoelliptic diffusion and subdiffusion equations
Michael Ruzhansky, Niyaz Tokmagambetov, Berikbol T. Torebek
A class of inverse problems for restoring the right-hand side of a parabolic equation for a large class of positive operators with discrete spectrum is considered. The results on e…
On a non-local problem for a multi-term fractional diffusion-wave equation
Michael Ruzhansky, Niyaz Tokmagambetov, Berikbol T. Torebek
This paper deals with the multi-term generalisation of the time-fractional diffusion-wave equation for general operators with discrete spectrum, as well as for positive hypoellipti…
Extremum principle for the Hadamard derivatives and its application to nonlinear fractional partial differential equations
Mokhtar Kirane, Berikbol T. Torebek
In this paper we obtain new estimates of the Hadamard fractional derivatives of a function at its extreme points. The extremum principle is then applied to show that the initial-bo…