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Global existence and blow-up of solutions to porous medium equation and pseudo-parabolic equation, I. Stratified groups

Michael Ruzhansky (UGent) , Bolys Sabitbek and Berikbol Torebek (UGent)
(2023) MANUSCRIPTA MATHEMATICA. 171. p.377-395
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Abstract
In this paper, we prove a global existence and blow-up of the positive solutions to the initial-boundary value problem of the nonlinear porous medium equation and the nonlinear pseudo-parabolic equation on the stratified Lie groups. Our proof is based on the concavity argument and the Poincare inequality, established in Ruzhansky and Suragan (J Differ Eq 262:1799-1821, 2017) for stratified groups.
Keywords
General Mathematics, NONEXISTENCE THEOREMS, ASYMPTOTIC-BEHAVIOR, CRITICAL EXPONENTS, HEAT-EQUATION, TIME, INEQUALITIES

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MLA
Ruzhansky, Michael, et al. “Global Existence and Blow-up of Solutions to Porous Medium Equation and Pseudo-Parabolic Equation, I. Stratified Groups.” MANUSCRIPTA MATHEMATICA, vol. 171, 2023, pp. 377–95, doi:10.1007/s00229-022-01390-2.
APA
Ruzhansky, M., Sabitbek, B., & Torebek, B. (2023). Global existence and blow-up of solutions to porous medium equation and pseudo-parabolic equation, I. Stratified groups. MANUSCRIPTA MATHEMATICA, 171, 377–395. https://doi.org/10.1007/s00229-022-01390-2
Chicago author-date
Ruzhansky, Michael, Bolys Sabitbek, and Berikbol Torebek. 2023. “Global Existence and Blow-up of Solutions to Porous Medium Equation and Pseudo-Parabolic Equation, I. Stratified Groups.” MANUSCRIPTA MATHEMATICA 171: 377–95. https://doi.org/10.1007/s00229-022-01390-2.
Chicago author-date (all authors)
Ruzhansky, Michael, Bolys Sabitbek, and Berikbol Torebek. 2023. “Global Existence and Blow-up of Solutions to Porous Medium Equation and Pseudo-Parabolic Equation, I. Stratified Groups.” MANUSCRIPTA MATHEMATICA 171: 377–395. doi:10.1007/s00229-022-01390-2.
Vancouver
1.
Ruzhansky M, Sabitbek B, Torebek B. Global existence and blow-up of solutions to porous medium equation and pseudo-parabolic equation, I. Stratified groups. MANUSCRIPTA MATHEMATICA. 2023;171:377–95.
IEEE
[1]
M. Ruzhansky, B. Sabitbek, and B. Torebek, “Global existence and blow-up of solutions to porous medium equation and pseudo-parabolic equation, I. Stratified groups,” MANUSCRIPTA MATHEMATICA, vol. 171, pp. 377–395, 2023.
@article{01H1BSN6HBAJ0XEFF5S8EMB326,
  abstract     = {{In this paper, we prove a global existence and blow-up of the positive solutions to the initial-boundary value problem of the nonlinear porous medium equation and the nonlinear pseudo-parabolic equation on the stratified Lie groups. Our proof is based on the concavity argument and the Poincare inequality, established in Ruzhansky and Suragan (J Differ Eq 262:1799-1821, 2017) for stratified groups.}},
  author       = {{Ruzhansky, Michael and Sabitbek, Bolys and Torebek, Berikbol}},
  issn         = {{0025-2611}},
  journal      = {{MANUSCRIPTA MATHEMATICA}},
  keywords     = {{General Mathematics,NONEXISTENCE THEOREMS,ASYMPTOTIC-BEHAVIOR,CRITICAL EXPONENTS,HEAT-EQUATION,TIME,INEQUALITIES}},
  language     = {{eng}},
  pages        = {{377--395}},
  title        = {{Global existence and blow-up of solutions to porous medium equation and pseudo-parabolic equation, I. Stratified groups}},
  url          = {{http://doi.org/10.1007/s00229-022-01390-2}},
  volume       = {{171}},
  year         = {{2023}},
}
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