E. I. Galakhov, “On the Absence of Local Solutions of Several Evolutionary Problems”, Mat. Zametki, 86:3 (2009), 337–349; Math. Notes, 86:3 (2009), 314

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Matematicheskie Zametki, 2009, Volume 86, Issue 3, Pages 337–349
DOI: https://doi.org/10.4213/mzm8498 (Mi mzm8498)

This article is cited in 10 scientific papers (total in 10 papers)

On the Absence of Local Solutions of Several Evolutionary Problems

E. I. Galakhov

Steklov Mathematical Institute, Russian Academy of Sciences

Full-text PDF (530 kB) Citations (10)

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DOI: https://doi.org/10.4213/mzm8498

Abstract: We consider the existence problem for local (with respect to time) solutions of quasilinear evolutionary partial differential equations and inequalities with singular coefficients and initial conditions. We obtain sufficient conditions for instantaneous blow-up of solutions and show that the results thus obtained cannot be improved in the function class under study.

Keywords: existence problem, quasilinear evolutionary PDE, weak solution, Dirichlet boundary condition, heat equation, Sobolev space, Carathéodory function.

Received: 27.10.2008

English version:
Mathematical Notes, 2009, Volume 86, Issue 3, Pages 314–324
DOI: https://doi.org/10.1134/S000143460909003X

Bibliographic databases:

UDC: 517.954

Language: Russian

Citation: E. I. Galakhov, “On the Absence of Local Solutions of Several Evolutionary Problems”, Mat. Zametki, 86:3 (2009), 337–349; Math. Notes, 86:3 (2009), 314–324

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Linking options:

https://www.mathnet.ru/eng/mzm8498

https://doi.org/10.4213/mzm8498

https://www.mathnet.ru/eng/mzm/v86/i3/p337

This publication is cited in the following 10 articles:

Meiirkhan B. Borikhanov, Michael Ruzhansky, Berikbol T. Torebek, “Instantaneous blow-up solutions for nonlinear Sobolev-type equations on the Heisenberg groups”, DCDS-S, 2024
V. E. Admasu, “On the absence of weak solutions of nonlinear nonnegative higher order parabolic inequalities with a nonlocal source”, Comput. Math. Math. Phys., 63:6 (2023), 1052–1063
Mohamed Jleli, Bessem Samet, “Instantaneous blow-up for nonlinear Sobolev type equations with potentials on Riemannian manifolds”, CPAA, 21:6 (2022), 2065
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
Jleli M., Samet B., “Instantaneous Blow-Up For a Fractional in Time Equation of Sobolev Type”, Math. Meth. Appl. Sci., 43:8 (2020), 5645–5652
M. O. Korpusov, A. A. Panin, “Instantaneous blow-up versus local solubility of the Cauchy problem for a two-dimensional equation of a semiconductor with heating”, Izv. Math., 83:6 (2019), 1174–1200
Korpusov M.O., Lukyanenko D.V., “Instantaneous Blow-Up Versus Local Solvability For One Problem of Propagation of Nonlinear Waves in Semiconductors”, J. Math. Anal. Appl., 459:1 (2018), 159–181
M. O. Korpusov, “On an instantaneous blow-up of solutions of evolutionary problems on the half-line”, Izv. Math., 82:5 (2018), 914–930
Korpusov M.O., Ovchinnikov A.V., Panin A.A., “Instantaneous Blow-Up Versus Local Solvability of Solutions to the Cauchy Problem For the Equation of a Semiconductor in a Magnetic Field”, Math. Meth. Appl. Sci., 41:17, SI (2018), 8070–8099
M. O. Korpusov, “Critical exponents of instantaneous blow-up or local solubility of non-linear equations of Sobolev type”, Izv. Math., 79:5 (2015), 955–1012

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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