INSTANTANEOUS BLOW-UP SOLUTIONS FOR NONLINEAR SOBOLEV-TYPE EQUATIONS ON THE HEISENBERG GROUPS

Borikhanov M.B. Ruzhansky M. Torebek B.T.
August 2025 American Institute of Mathematical Sciences

Discrete and Continuous Dynamical Systems - Series S
2025 #18 Issue 8 2127 - 2141 pp.

In this paper, we study two nonlinear Sobolev-type equations on the Heisenberg groups. We show that the problems do not admit nontrivial local weak solutions, i.e. “instantaneous blow-up” occurs, using the nonlinear capacity method. Namely, by choosing suitable test functions, we will prove an instantaneous blow-up for any initial conditions u0, u1 ∈ L^q(Hⁿ) with q ≤ _Q^Q₋₂.

critical exponents global existence , Heisenberg group , instantaneous blow-up , Nonlinear Sobolev-type equations

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Khoja Akhmet Yassawi International Kazakh-Turkish University, Sattarkhanov ave., 29, Turkistan, 161200, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Belgium
School of Mathematical Sciences, Queen Mary University of London, United Kingdom

Khoja Akhmet Yassawi International Kazakh-Turkish University
Institute of Mathematics and Mathematical Modeling
Department of Mathematics: Analysis
School of Mathematical Sciences

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