Local Solvability and Decay of the Solution of an Equation with Quadratic Noncoercive Nonlineatity

Корпусов, М. О.; Lukyanenko, D. V.; Ovsyannikov, E. A.; Panin, Alexander Anatolyevich

doi:10.14529/mmp170209

Cited by 6 publications

(3 citation statements)

References 8 publications

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“…Remark As a possible further evolvement of the present work, we can suggest the development of numerical method (see our papers()) that allows to detect the instantaneous blow‐up. But we have to notice that, in case of absence of a priori information obtained (as in the present paper) analytically, numerical calculation is not a rigorous proof that instantaneous blow‐up really occurs.…”

Section: Cauchy Problemmentioning

confidence: 81%

“…First, we consider the case where 1 < q < 3; then 3 − 2q ′ < 0 and 3∕q ′ − 2 < 0. Setting R = N in the inequality (24), passing to the limit as N → + ∞ and taking into account (29), (21) to (23), and (28), we obtain the equality…”

Section: Definitionmentioning

confidence: 99%

“…Thus, the theorem is completely proved. [20][21][22][23][24] ) that allows to detect the instantaneous blow-up. But we have to notice that, in case of absence of a priori information obtained (as in the present paper) analytically, numerical calculation is not a rigorous proof that instantaneous blow-up really occurs.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Instantaneous blow‐up versus local solvability of solutions to the Cauchy problem for the equation of a semiconductor in a magnetic field

Корпусов

Овчинников

Panin

2018

Math Methods in App Sciences

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Section: Cauchy Problemmentioning

confidence: 81%

Section: Definitionmentioning

confidence: 99%

See 1 more Smart Citation

Instantaneous blow‐up versus local solvability of solutions to the Cauchy problem for the equation of a semiconductor in a magnetic field

Корпусов

Овчинников

Panin

2018

Math Methods in App Sciences

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

Корпусов¹,

Панин²,

Shishkov³

2021

Izv. Math.

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We consider the Cauchy problem for a model partial differential equation of order three with a non-linearity of the form . We prove that when the Cauchy problem in has no local-in-time weak solution for a large class of initial functions, while when there is a local weak solution.

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Diagnostics of Instant Decomposition of Solution in the Nonlinear Equation of Theory of Waves in Semiconductors

Корпусов¹,

Matveeva²,

Lukyanenko³

2019

Bulletin SUSU MMP

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В работе рассматривается метод численной диагностики разрушения решения в нелинейном уравнении теории волн в полупроводниках. Особенность рассматриваемой задачи заключается в том, что на положительной полупрямой отсутствует даже локальное во времени слабое решение задачи, в то время как на отрезке от 0 до L существует локальное во времени классическое решение. Нашей задачей являлось численно показать, что при L, стремящемся к бесконечности, время существования решения стремится к нулю. Численная диагностика разрушения решения основана на методике вычисления апостериорной асимптотически точной оценки погрешности полученного численного решения по методике Ричардсона.Ключевые слова: численная диагностика мгновенного разрушения решения.

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Local Solvability and Decay of the Solution of an Equation with Quadratic Noncoercive Nonlineatity

Cited by 6 publications

References 8 publications

Instantaneous blow‐up versus local solvability of solutions to the Cauchy problem for the equation of a semiconductor in a magnetic field

Instantaneous blow‐up versus local solvability of solutions to the Cauchy problem for the equation of a semiconductor in a magnetic field

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

Diagnostics of Instant Decomposition of Solution in the Nonlinear Equation of Theory of Waves in Semiconductors

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