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Teoreticheskaya i Matematicheskaya Fizika, 2021, Volume 207, Number 3, Pages 361–375
DOI: https://doi.org/10.4213/tmf10036 (Mi tmf10036) 		 
Fourier transformation method for some types of nonlinear partial differential equations

V. I. Gishlarkaev

Chechen State University, Groznyi, Russia
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DOI: https://doi.org/10.4213/tmf10036
Abstract: We propose a method for analyzing the Cauchy problem for a wide class of equations with power-like nonlinearities. The method is based on the Fourier transformation, which allows reducing the original equation to an integro-differential one. We prove the existence of solutions.
Keywords: equations with power-like nonlinearities, Fourier transformation, integro-differential equation, Paley–Wiener–Schwarz theorems on Fourier image.
Received: 15.12.2020
Revised: 15.12.2020
English version:
Theoretical and Mathematical Physics, 2021, Volume 207, Issue 3, Pages 713–726
DOI: https://doi.org/10.1134/S0040577921060039
Bibliographic databases:
Document Type: Article
MSC: 35G25
Language: Russian
Citation: V. I. Gishlarkaev, “Fourier transformation method for some types of nonlinear partial differential equations”, TMF, 207:3 (2021), 361–375; Theoret. and Math. Phys., 207:3 (2021), 713–726
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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