Abstract
The Cauchy problem for a model nonlinear equation with gradient nonlinearity is considered. We prove the existence of two critical exponents, \({{q}_{1}} = 2\) and \({{q}_{2}} = 3\), such that this problem has no local-in-time weak (in some sense) solution for \(1 < q\;\leqslant \;{{q}_{1}}\), while such a solution exists for \(q > {{q}_{1}}\), but, for \({{q}_{1}} < q\;\leqslant \;{{q}_{2}}\), there is no global-in-time weak solution.
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Funding
This work was supported by the Foundation for Advancement of Theoretical Physics and Mathematics “BASIS” and by the Russian Science Foundation (project no. 23-11-00056), RUDN University.
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Translated by I. Ruzanova
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Korpusov, M.O., Matveeva, A.K. On Critical Exponents for Weak Solutions of the Cauchy Problem for a (2 + 1)-Dimensional Nonlinear Composite-Type Equation with Gradient Nonlinearity. Comput. Math. and Math. Phys. 63, 1070–1084 (2023). https://doi.org/10.1134/S096554252306012X
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DOI: https://doi.org/10.1134/S096554252306012X