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Pregled bibliografske jedinice broj: 804103

A family of fourth-order q-logarithmic equations


Bukal, Mario
A family of fourth-order q-logarithmic equations // Journal of mathematical analysis and applications, 438 (2016), 1; 142-161 doi:10.1016/j.jmaa.2016.02.002 (međunarodna recenzija, članak, znanstveni)


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Naslov
A family of fourth-order q-logarithmic equations

Autori
Bukal, Mario

Izvornik
Journal of mathematical analysis and applications (0022-247X) 438 (2016), 1; 142-161

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
fourth-order diffusion equations ; tsallis entropy ; entropy–entropy dissipation method ; existence of weak solutions ; long-time behaviour of solutions

Sažetak
We prove the existence of global in time weak nonnegative solutions to a family of nonlinear fourth-order evolution equations, parametrized by a real parameter q∈(0, 1], which includes the well known thin-film (q=1/2) and the Derrida–Lebowitz– Speer–Spohn (DLSS) equation (q=1), subject to periodic boundary conditions in one spatial dimension. In contrast to the gradient flow approach in [25], our method relies on dissipation property of the corresponding entropy functionals (Tsallis entropies) resulting in required a priori estimates, and extends the existence result from [25] to a wider range of the family members, namely to 0<q<1/2. Generalized Beckner-type functional inequalities yield an exponential decay rate of (relative) entropies, which in further implies the exponential stability in the L1-norm of the constant steady state. Finally, we provide illustrative numerical examples supporting the analytical results.

Izvorni jezik
Engleski

Znanstvena područja
Matematika



POVEZANOST RADA


Projekti:
HRZZ-UIP-2013-11-9477 - MAtematička analiza multifizikalnih problema koji uključuju tanke i kompozitne strukture i fluide (MAMPITCoStruFl) (Velčić, Igor, HRZZ - 2013-11) ( POIROT)

Ustanove:
Fakultet elektrotehnike i računarstva, Zagreb

Profili:

Avatar Url Mario Bukal (autor)

Citiraj ovu publikaciju

Bukal, Mario
A family of fourth-order q-logarithmic equations // Journal of mathematical analysis and applications, 438 (2016), 1; 142-161 doi:10.1016/j.jmaa.2016.02.002 (međunarodna recenzija, članak, znanstveni)
Bukal, M. (2016) A family of fourth-order q-logarithmic equations. Journal of mathematical analysis and applications, 438 (1), 142-161 doi:10.1016/j.jmaa.2016.02.002.
@article{article, author = {Bukal, M.}, year = {2016}, pages = {142-161}, DOI = {10.1016/j.jmaa.2016.02.002}, keywords = {fourth-order diffusion equations, tsallis entropy, entropy–entropy dissipation method, existence of weak solutions, long-time behaviour of solutions}, journal = {Journal of mathematical analysis and applications}, doi = {10.1016/j.jmaa.2016.02.002}, volume = {438}, number = {1}, issn = {0022-247X}, title = {A family of fourth-order q-logarithmic equations}, keyword = {fourth-order diffusion equations, tsallis entropy, entropy–entropy dissipation method, existence of weak solutions, long-time behaviour of solutions} }
@article{article, author = {Bukal, M.}, year = {2016}, pages = {142-161}, DOI = {10.1016/j.jmaa.2016.02.002}, keywords = {fourth-order diffusion equations, tsallis entropy, entropy–entropy dissipation method, existence of weak solutions, long-time behaviour of solutions}, journal = {Journal of mathematical analysis and applications}, doi = {10.1016/j.jmaa.2016.02.002}, volume = {438}, number = {1}, issn = {0022-247X}, title = {A family of fourth-order q-logarithmic equations}, keyword = {fourth-order diffusion equations, tsallis entropy, entropy–entropy dissipation method, existence of weak solutions, long-time behaviour of solutions} }

Časopis indeksira:


  • Current Contents Connect (CCC)
  • Web of Science Core Collection (WoSCC)
    • Science Citation Index Expanded (SCI-EXP)
    • SCI-EXP, SSCI i/ili A&HCI
  • Scopus


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