A Method of Verified Computations for Solutions to Semilinear Parabolic Equations Using Semigroup Theory

Makoto Mizuguchi; Akitoshi Takayasu; Takayuki Kubo; Shin'ichi Oishi

doi:10.1137/141001664

A Method of Verified Computations for Solutions to Semilinear Parabolic Equations Using Semigroup Theory

SIAM Journal on Numerical Analysis ◽

10.1137/141001664 ◽

2017 ◽

Vol 55 (2) ◽

pp. 980-1001 ◽

Cited By ~ 5

Author(s):

Makoto Mizuguchi ◽

Akitoshi Takayasu ◽

Takayuki Kubo ◽

Shin'ichi Oishi

Keyword(s):

Parabolic Equations ◽

Semigroup Theory ◽

Semilinear Parabolic Equations ◽

Verified Computations ◽

Semilinear Parabolic

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Verified Computations for Solutions to Semilinear Parabolic Equations Using the Evolution Operator

Mathematical Aspects of Computer and Information Sciences - Lecture Notes in Computer Science ◽

10.1007/978-3-319-32859-1_18 ◽

2016 ◽

pp. 218-223 ◽

Cited By ~ 1

Author(s):

Akitoshi Takayasu ◽

Makoto Mizuguchi ◽

Takayuki Kubo ◽

Shin’ichi Oishi

Keyword(s):

Parabolic Equations ◽

Evolution Operator ◽

Semilinear Parabolic Equations ◽

Verified Computations ◽

Semilinear Parabolic

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Global Existence, Exponential Decay and Blow-up in Finite Time for a Class of Finitely Degenerate Semilinear Parabolic Equations

Acta Mathematica Scientia ◽

10.1007/s10473-019-0508-8 ◽

2019 ◽

Vol 39 (5) ◽

pp. 1290-1308 ◽

Cited By ~ 1

Author(s):

Hua Chen ◽

Huiyang Xu

Keyword(s):

Global Existence ◽

Exponential Decay ◽

Parabolic Equations ◽

Finite Time ◽

Blow Up ◽

Semilinear Parabolic Equations ◽

Semilinear Parabolic

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Global existence and local continuity of solutions for semilinear parabolic equations

Communications in Partial Differential Equations ◽

10.1080/03605309708821310 ◽

1997 ◽

Vol 22 (9-10) ◽

pp. 1529-1557 ◽

Cited By ~ 14

Author(s):

S. Zhang

Keyword(s):

Global Existence ◽

Parabolic Equations ◽

Semilinear Parabolic Equations ◽

Continuity Of Solutions ◽

Semilinear Parabolic

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Asymptotic behavior and blow up of solutions for semilinear parabolic equations at critical energy level

Mathematics and Computers in Simulation ◽

10.1016/j.matcom.2009.08.028 ◽

2009 ◽

Vol 80 (4) ◽

pp. 808-813 ◽

Cited By ~ 10

Author(s):

Xu Runzhang

Keyword(s):

Asymptotic Behavior ◽

Energy Level ◽

Parabolic Equations ◽

Blow Up ◽

Critical Energy ◽

Semilinear Parabolic Equations ◽

Semilinear Parabolic

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Boundedness and Almost Periodicity of Solutions for a Class of Semilinear Parabolic Equations with Boundary Degeneracy

Chinese Annals of Mathematics Series B ◽

10.1007/s11401-020-0200-2 ◽

2020 ◽

Vol 41 (2) ◽

pp. 303-324

Author(s):

Yi Xie ◽

Peidong Lei

Keyword(s):

Parabolic Equations ◽

Almost Periodicity ◽

Semilinear Parabolic Equations ◽

Boundary Degeneracy ◽

Semilinear Parabolic

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Exact decay estimates for solutions to semilinear parabolic equations

Applicable Analysis ◽

10.1080/00036819108840034 ◽

1991 ◽

Vol 42 (1-4) ◽

pp. 69-81 ◽

Cited By ~ 7

Author(s):

J.M. Ghidaglia ◽

A. Marzocchi

Keyword(s):

Parabolic Equations ◽

Decay Estimates ◽

Semilinear Parabolic Equations ◽

Semilinear Parabolic

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Asymptotics of eigenvalues of the Jacobi matrix of a system of semilinear parabolic equations

Mathematical Notes ◽

10.1134/s0001434611010263 ◽

2011 ◽

Vol 89 (1-2) ◽

pp. 206-213

Author(s):

A. S. Bratus’ ◽

M. V. Safro

Keyword(s):

Parabolic Equations ◽

Jacobi Matrix ◽

Semilinear Parabolic Equations ◽

Asymptotics Of Eigenvalues ◽

Semilinear Parabolic

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Heteroclinic Orbits of Semilinear Parabolic Equations

Journal of Differential Equations ◽

10.1006/jdeq.1996.0031 ◽

1996 ◽

Vol 125 (1) ◽

pp. 239-281 ◽

Cited By ~ 55

Author(s):

Bernold Fiedler ◽

Carlos Rocha

Keyword(s):

Parabolic Equations ◽

Heteroclinic Orbits ◽

Semilinear Parabolic Equations ◽

Semilinear Parabolic

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Optimal control problems governed by some semilinear parabolic equations

Nonlinear Analysis ◽

10.1016/j.na.2003.09.013 ◽

2004 ◽

Vol 56 (2) ◽

pp. 241-252 ◽

Cited By ~ 11

Author(s):

Sang-Uk Ryu

Keyword(s):

Optimal Control ◽

Parabolic Equations ◽

Optimal Control Problems ◽

Control Problems ◽

Semilinear Parabolic Equations ◽

Semilinear Parabolic

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Linear and Semilinear Parabolic Equations on BUC(ℝN)

Mathematische Nachrichten ◽

10.1002/mana.19961790108 ◽

1996 ◽

Vol 179 (1) ◽

pp. 107-118 ◽

Cited By ~ 8

Author(s):

Matthias Hieber ◽

Pablo Koch - Medina ◽

Sandro Merino

Keyword(s):

Parabolic Equations ◽

Semilinear Parabolic Equations ◽

Semilinear Parabolic

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