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Volume 25, Issue 1
Non-existence of Global Solutions for a Fractional Wave-diffusion Equations

Mohamed Berbiche & Ali Hakem

DOI: 10.4208/jpde.v25.n1.1

J. Part. Diff. Eq., 25 (2012), pp. 1-20.

Published online: 2012-03

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  • Abstract

We considered the Cauchy problem for the fractional wave-diffusion equation $$D^αu-Δ|u|^{m-1}u+(-Δ)^{β/2}D^γ|u|^{l-1}u=h(x,t)|u|^p+f(x,t)$$ with given initial data and where p > 1, 1 < α < 2, 0 < β < 2, 0 < γ < 1. Nonexistence results and necessary conditions for global existence are established by means of the test function method. This results extend previous works.

  • Keywords

Nonlinear wave-diffusion equation fractional power derivative critical exponent

  • AMS Subject Headings

35L20, 35L70, 34A12

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

berbichemed@yahoo.fr (Mohamed Berbiche)

hakemali@yahoo.com (Ali Hakem)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-25-1, author = {Berbiche , Mohamed and Hakem , Ali}, title = {Non-existence of Global Solutions for a Fractional Wave-diffusion Equations}, journal = {Journal of Partial Differential Equations}, year = {2012}, volume = {25}, number = {1}, pages = {1--20}, abstract = {

We considered the Cauchy problem for the fractional wave-diffusion equation $$D^αu-Δ|u|^{m-1}u+(-Δ)^{β/2}D^γ|u|^{l-1}u=h(x,t)|u|^p+f(x,t)$$ with given initial data and where p > 1, 1 < α < 2, 0 < β < 2, 0 < γ < 1. Nonexistence results and necessary conditions for global existence are established by means of the test function method. This results extend previous works.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v25.n1.1}, url = {http://global-sci.org/intro/article_detail/jpde/5171.html} }
TY - JOUR T1 - Non-existence of Global Solutions for a Fractional Wave-diffusion Equations AU - Berbiche , Mohamed AU - Hakem , Ali JO - Journal of Partial Differential Equations VL - 1 SP - 1 EP - 20 PY - 2012 DA - 2012/03 SN - 25 DO - http://doi.org/10.4208/jpde.v25.n1.1 UR - https://global-sci.org/intro/article_detail/jpde/5171.html KW - Nonlinear wave-diffusion equation KW - fractional power derivative KW - critical exponent AB -

We considered the Cauchy problem for the fractional wave-diffusion equation $$D^αu-Δ|u|^{m-1}u+(-Δ)^{β/2}D^γ|u|^{l-1}u=h(x,t)|u|^p+f(x,t)$$ with given initial data and where p > 1, 1 < α < 2, 0 < β < 2, 0 < γ < 1. Nonexistence results and necessary conditions for global existence are established by means of the test function method. This results extend previous works.

Mohamed Berbiche & Ali Hakem. (2019). Non-existence of Global Solutions for a Fractional Wave-diffusion Equations. Journal of Partial Differential Equations. 25 (1). 1-20. doi:10.4208/jpde.v25.n1.1
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