Geodesic
Fourier transformation method for some types of nonlinear partial differential equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 3, pp. 361-375

Voir la notice de l'article provenant de la source Math-Net.Ru

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, integro-differential equation, Paley–Wiener–Schwarz theorems on Fourier image.
Mots-clés : Fourier transformation 
@article{TMF_2021_207_3_a2,
     author = {V. I. Gishlarkaev},
     title = {Fourier transformation method for some types of nonlinear partial differential equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {361--375},
     publisher = {mathdoc},
     volume = {207},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_207_3_a2/}
}
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V. I. Gishlarkaev. Fourier transformation method for some types of nonlinear partial differential equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 3, pp. 361-375. http://geodesic.mathdoc.fr/item/TMF_2021_207_3_a2/