4 papers · 1 filter
Fujita exponents on quantum Euclidean spaces
Edward McDonald, Michael Ruzhansky, Serikbol Shaimardan +1
We study the well-posedness of a non-linear heat equation with power nonlinearity with positive initial data on quantum Euclidean spaces. We prove a noncommutative analogue of the…
On the -analogue of Duhamel's principle
Mohammed Elamine Sebih, Serikbol Shaimardan, Irfan Ali
In this paper, we revisit the classical Duhamel's principle and provide a self-contained proof of this fundamental tool for linear evolution equations and systems of coupled equati…
Sobolev inequality and its applications to nonlinear PDE on noncommutative Euclidean spaces
Michael Ruzhansky, Serikbol Shaimardan, Kanat Tulenov
In this work, we study the Sobolev inequality on noncommutative Euclidean spaces. As a simple consequence, we obtain the Gagliardo-Nirenberg type inequality and as its application…
Fourier multipliers and their applications to PDE on the quantum Euclidean space
M. Ruzhansky, S. Shaimardan, K. Tulenov
In this work, we present some applications of the - boundedness of Fourier multipliers to PDEs on the noncommutative (or quantum) Euclidean space. More precisely, we esta…