M. O. Korpusov, A. A. Panin, A. E. Shishkov, “On the critical exponent “instantaneous blow-up” versus “local solubility” in the Cauchy problem for a model equation of Sobolev type”, Izv. Math., 85:1 (2021), 111

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Izvestiya: Mathematics, 2021, Volume 85, Issue 1, Pages 111–144
DOI: https://doi.org/10.1070/IM8949 (Mi im8949)

This article is cited in 15 scientific papers (total in 15 papers)

On the critical exponent “instantaneous blow-up” versus “local solubility” in the Cauchy problem for a model equation of Sobolev type

M. O. Korpusov^a, A. A. Panin^a, A. E. Shishkov^b

^a Faculty of Physics, Lomonosov Moscow State University
^b Peoples' Friendship University of Russia, Moscow

English version PDF (662 kB) Citations (15) Russian version article

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DOI: https://doi.org/10.1070/IM8949

Abstract: We consider the Cauchy problem for a model partial differential equation of order three with a non-linearity of the form $|\nabla u|^q$. We prove that when $q\in(1,3/2]$ the Cauchy problem in $\mathbb{R}^3$ has no local-in-time weak solution for a large class of initial functions, while when $q>3/2$ there is a local weak solution.

Keywords: finite-time blow-up, non-linear waves, instantaneous blow-up.

Funding agency	Grant number
Russian Science Foundation	18-11-00042
Ministry of Education and Science of the Russian Federation	5-100
This paper was written with the support of the PFUR Programme “5-100” (Korpusov, Shishkov) and Russian Science Foundation grant no. 18-11-00042 (Panin).

Received: 02.07.2019

Bibliographic databases:

Document Type: Article

UDC: 517.957

MSC: 35B44, 35G25

Language: English

Original paper language: Russian

Citation: M. O. Korpusov, A. A. Panin, A. E. Shishkov, “On the critical exponent “instantaneous blow-up” versus “local solubility” in the Cauchy problem for a model equation of Sobolev type”, Izv. Math., 85:1 (2021), 111–144

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This publication is cited in the following 15 articles:

M. V. Artemeva, M. O. Korpusov, A. A. Panin, “On the solvability of the Cauchy problem for a thermal–electrical model”, Theoret. and Math. Phys., 222:2 (2025), 183–197
Tahir Shahzad, Muhammad O. Ahmed, Muhammad Sajid Iqbal, Muhammad Zafarullah Baber, Muhammad Waqas Yasin, A. S. A. Alsubaie, K. H. Mahmoud, Mustafa Inc, “Explicit solitary wave solutions for the nonlinear equations in semiconductor and magnetic field with their stability analysis”, Opt Quant Electron, 56:1 (2024)
M. V. Artemeva, M. O. Korpusov, “On the Existence of a Nonextendable Solution of the Cauchy problem for a $(1+1)$-Dimensional Thermal-Electrical Model”, Math. Notes, 115:5 (2024), 653–663
M. V. Artemeva, M. O. Korpusov, “On the blow-up of the solution of a $(1+1)$-dimensional thermal–electrical model”, Theoret. and Math. Phys., 219:2 (2024), 748–760
Meiirkhan B. Borikhanov, Michael Ruzhansky, Berikbol T. Torebek, “Instantaneous blow-up solutions for nonlinear Sobolev-type equations on the Heisenberg groups”, DCDS-S, 2024
M. V Artemeva, M. O Korpusov, “THE CAUCHY PROBLEM FOR AN NONLINEAR WAVE EQUATION”, Differencialʹnye uravneniâ, 60:10 (2024), 1299
M. V. Artemeva, M. O. Korpusov, “On the existence of a nonextendable solution of the Cauchy problem for a $(3+1)$-dimensional thermal–electrical model”, Theoret. and Math. Phys., 221:3 (2024), 2207–2218
M. V. Artemeva, M. O. Korpusov, “The Cauchy Problem for a Nonlinear Wave Equation”, Diff Equat, 60:10 (2024), 1369
M. O. Korpusov, A. Yu. Perlov, A. V. Tymoshenko, R. S. Shafir, “Global-in-time solvability of a nonlinear system of equations of a thermal–electrical model with quadratic nonlinearity”, Theoret. and Math. Phys., 217:2 (2023), 1743–1754
M. O. Korpusov, A. Yu. Perlov, A. V. Tymoshenko, R. S. Shafir, “On the Blow-Up of the Solution of a Nonlinear System of Equations of a Thermal-Electrical Model”, Math. Notes, 114:5 (2023), 850–861
A. V. Keller, “Sobolev-type systems and applied problems”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 16:4 (2023), 5–32
N. A. Manakova, O. V. Gavrilova, K. V. Perevozhikova, “Semilinear models of Sobolev type. Non-uniqueness of solution to the Showalter–Sidorov problem”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 15:1 (2022), 84–100
Korpusov M.O. Panin A.A., “On the Blow-Up of the Solution and on the Local and Global Solvability of the Cauchy Problem For a Nonlinear Equation in Holder Spaces”, J. Math. Anal. Appl., 504:2 (2021), 125469
Zamyshlyaeva A., Lut A., “Inverse Problem For the Sobolev Type Equation of Higher Order”, Mathematics, 9:14 (2021), 1647
M. O. Korpusov, G. I. Shlyapugin, “O razrushenii reshenii zadach Koshi dlya odnogo klassa nelineinykh uravnenii teorii ferritov”, Materialy Vserossiiskoi nauchnoi konferentsii «Differentsialnye uravneniya i ikh prilozheniya», posvyaschennoi 85-letiyu professora M. T. Terekhina. Ryazanskii gosudarstvennyi universitet im. S.A. Esenina, Ryazan, 17–18 maya 2019 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 185, VINITI RAN, M., 2020, 79–131

Citing articles in Google Scholar: Russian citations, English citations
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References:	80
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