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Solvability to some strongly degenerate parabolic problems. / Lavrentiev, Mikhail M.; Tani, Atusi.

In: Journal of Mathematical Analysis and Applications, Vol. 475, No. 1, 01.07.2019, p. 576-594.

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Harvard

Lavrentiev, MM & Tani, A 2019, 'Solvability to some strongly degenerate parabolic problems', Journal of Mathematical Analysis and Applications, vol. 475, no. 1, pp. 576-594. https://doi.org/10.1016/j.jmaa.2019.02.056

APA

Lavrentiev, M. M., & Tani, A. (2019). Solvability to some strongly degenerate parabolic problems. Journal of Mathematical Analysis and Applications, 475(1), 576-594. https://doi.org/10.1016/j.jmaa.2019.02.056

Vancouver

Lavrentiev MM, Tani A. Solvability to some strongly degenerate parabolic problems. Journal of Mathematical Analysis and Applications. 2019 Jul 1;475(1):576-594. doi: 10.1016/j.jmaa.2019.02.056

Author

Lavrentiev, Mikhail M. ; Tani, Atusi. / Solvability to some strongly degenerate parabolic problems. In: Journal of Mathematical Analysis and Applications. 2019 ; Vol. 475, No. 1. pp. 576-594.

BibTeX

@article{96953a8f322b4994848b512ec6b13f0f,
title = "Solvability to some strongly degenerate parabolic problems",
abstract = " Nonlinear parabolic equations of “divergence form,” u t =(φ(u)ψ(u x )) x , are considered under the assumption that the “material flux,” φ(u)ψ(v), is bounded for all values of arguments, u and v. In literature such equations have been referred to as “strongly degenerate” equations. This is due to the fact that the coefficient, φ(u)ψ ′ (u x ), of the second derivative, u xx , can be arbitrarily small for large value of the gradient, u x . The “hyperbolic phenomena” (unbounded growth of space derivatives within a finite time) have been established in literature for solutions to Cauchy problem for the above-mentioned equations. Accordingly one can expect a correct statement of the initial-boundary value problem for such equations only under additional assumptions on the problem data. In this paper we describe several restrictions, under which the initial-boundary value problems for strongly degenerate parabolic equations are well-posed. ",
keywords = "Generalized distance, Global-in-time solutions, Hyperbolic phenomena, Initial-boundary value problem, Strongly degenerate parabolic equations, HEAT, BOUNDARY, BLOW-UP",
author = "Lavrentiev, {Mikhail M.} and Atusi Tani",
year = "2019",
month = jul,
day = "1",
doi = "10.1016/j.jmaa.2019.02.056",
language = "English",
volume = "475",
pages = "576--594",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "1",

}

RIS

TY - JOUR

T1 - Solvability to some strongly degenerate parabolic problems

AU - Lavrentiev, Mikhail M.

AU - Tani, Atusi

PY - 2019/7/1

Y1 - 2019/7/1

N2 - Nonlinear parabolic equations of “divergence form,” u t =(φ(u)ψ(u x )) x , are considered under the assumption that the “material flux,” φ(u)ψ(v), is bounded for all values of arguments, u and v. In literature such equations have been referred to as “strongly degenerate” equations. This is due to the fact that the coefficient, φ(u)ψ ′ (u x ), of the second derivative, u xx , can be arbitrarily small for large value of the gradient, u x . The “hyperbolic phenomena” (unbounded growth of space derivatives within a finite time) have been established in literature for solutions to Cauchy problem for the above-mentioned equations. Accordingly one can expect a correct statement of the initial-boundary value problem for such equations only under additional assumptions on the problem data. In this paper we describe several restrictions, under which the initial-boundary value problems for strongly degenerate parabolic equations are well-posed.

AB - Nonlinear parabolic equations of “divergence form,” u t =(φ(u)ψ(u x )) x , are considered under the assumption that the “material flux,” φ(u)ψ(v), is bounded for all values of arguments, u and v. In literature such equations have been referred to as “strongly degenerate” equations. This is due to the fact that the coefficient, φ(u)ψ ′ (u x ), of the second derivative, u xx , can be arbitrarily small for large value of the gradient, u x . The “hyperbolic phenomena” (unbounded growth of space derivatives within a finite time) have been established in literature for solutions to Cauchy problem for the above-mentioned equations. Accordingly one can expect a correct statement of the initial-boundary value problem for such equations only under additional assumptions on the problem data. In this paper we describe several restrictions, under which the initial-boundary value problems for strongly degenerate parabolic equations are well-posed.

KW - Generalized distance

KW - Global-in-time solutions

KW - Hyperbolic phenomena

KW - Initial-boundary value problem

KW - Strongly degenerate parabolic equations

KW - HEAT

KW - BOUNDARY

KW - BLOW-UP

UR - http://www.scopus.com/inward/record.url?scp=85062230851&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2019.02.056

DO - 10.1016/j.jmaa.2019.02.056

M3 - Article

AN - SCOPUS:85062230851

VL - 475

SP - 576

EP - 594

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -

ID: 18678252