3 citations · 3 across the 9 of their papers we have counts for
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Fujita exponent for heat equation with Hörmander vector fields
Marianna Chatzakou, Aidyn Kassymov, Michael Ruzhansky
In this paper, we show global existence and non-existence results for the heat equation with some of the squares of smooth vector fields on $\Rn$ satisfying Hörmander's rank condit…
Zero modes and Dirac-(logarithmic) Sobolev-type inequalities
Marianna Chatzakou, Uwe Kahler, Michael Ruzhansky
We study the decay rate of the zero modes of the Dirac operator with a matrix-valued potential that is considered here without any regularity assumptions, compared to the existing…
Nearness and solvability of non-invariant equations on stratified groups
Marianna Chatzakou, Michael Ruzhansky, Nikos Yannakakis
We prove the well-posedness of the differential equation in the setting of a stratified group when the considered second-order differential operator can be…
On global solutions of heat equations with time-dependent nonlinearities on unimodular Lie groups
Marianna Chatzakou, Aidyn Kassymov, Michael Ruzhansky
In this work, we study the global well-posedeness of the heat equation with variable time-dependent nonlinearity of the form on unimodular Lie groups when the differenti…
Anharmonic semigroups and applications to global well-posedness of nonlinear heat equations
Duván Cardona, Marianna Chatzakou, Julio Delgado +2
In this work we consider the semigroup for associated to an anharmonic oscillator of the form …
Logarithmic Sobolev, Hardy and Poincaré inequalities on the Heisenberg group
Marianna Chatzakou, Aidyn Kassymov, Michael Ruzhansky
In this paper we first prove a number of important inequalities with explicit constants in the setting of the Heisenberg group. This includes the fractional and integer Sobolev, Ga…