Geodesic
Global existence and stability of solution for a nonlinear Kirchhoff type reaction-diffusion equation with variable exponents
Mathematica Bohemica, Tome 147 (2022) no. 4, pp. 471-484

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We consider a class of Kirchhoff type reaction-diffusion equations with variable exponents and source terms \begin {equation*} u_{t}-M\biggl (\int _\Omega \vert \nabla u \vert ^{2} {\rm d}x\bigg ) \Delta u+ \vert u \vert ^{m(x) -2}u_{t}= \vert u \vert ^{r(x) -2}u. \end {equation*} We prove with suitable assumptions on the variable exponents $r( {\cdot }),$ $m({\cdot })$ the global existence of the solution and a stability result using potential and Nihari's functionals with small positive initial energy, the stability being based on Komornik's inequality.
DOI : 10.21136/MB.2021.0122-20
Classification : 35B40, 35L10, 35L70
Keywords: Kirchhoff equation; reaction-diffusion equation; variable exponent; global solution 
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Khaldi, Aya; Ouaoua, Amar; Maouni, Messaoud. Global existence and stability of solution for a nonlinear Kirchhoff type reaction-diffusion equation with variable exponents. Mathematica Bohemica, Tome 147 (2022) no. 4, pp. 471-484. doi: 10.21136/MB.2021.0122-20

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