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Nonlinear Evolution Equations: Blow-up, Stability, Asymptotic Behavior by Benkouider, Soufiane

Nonlinear Evolution Equations: Blow-up, Stability, Asymptotic Behavior

by Soufiane Benkouider , Said Mekhdoua
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Book cover type: Paperback
  • ISBN13: 9786202431774
  • Binding: Paperback
  • Subject: N/A
  • Publisher: LAP Lambert Academic Publishing
  • Publisher Imprint: LAP Lambert Academic Publishing
  • Publication Date:
  • Pages: 144
  • Original Price: GBP 59.94
  • Language: English
  • Edition: N/A
  • Item Weight: 200 grams
  • BISAC Subject(s): General

This book investigates the blow-up phenomena, asymptotic behavior, and stability ofsolutions for several classes of nonlinear partial differential equations (PDEs), includingreaction-diffusion and wave-type equations with variable exponents, memory effects, andsingular coeffcients. The work is divided into four main parts.First, we study the blow-up phenomenon for nondegenerate parabolic PDEs in boundeddomains. By considering a nonnegative diffusion coeffcient a(x, t), we establish new blowup criteria and derive sharp lower and upper bounds for the blow-up time of semilinearreaction-diffusion equations and nonlinear equations involving the m(x, t)-Laplacian operator.Second, we analyze the initial-boundary value problem for Kirchhoff-type viscoelasticwave equations with Balakrishnan-Taylor damping, infinite memory, and time-varyingdelay. Under suitable assumptions on the relaxation function and initial data, we provethat the energy decays at a rate determined by the relaxation function, which may beneither exponential nor polynomial. Moreover, we establish a general stability resultunder a weak growth condition on the relaxation kernel.

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