{"product_id":"nonlinear-evolution-equations-blow-up-stability-asymptotic-behavior-9786202431774","title":"Nonlinear Evolution Equations: Blow-up, Stability, Asymptotic Behavior","description":"\u003cp\u003e • Author(s): Soufiane Benkouider | Said Mekhdoua\u003cbr\u003e • Publisher: LAP Lambert Academic Publishing\u003cbr\u003e • Publisher Imprint: LAP Lambert Academic Publishing\u003cbr\u003e • BISAC: General\u003c\/p\u003e\u003cp\u003eThis 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.\u003c\/p\u003e","brand":"Atlantic Books","offers":[{"title":"Paperback","offer_id":46377271328919,"sku":"9786202431774","price":6651.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9786202431774.webp?v=1768760507","url":"https:\/\/atlanticbooks.com\/products\/nonlinear-evolution-equations-blow-up-stability-asymptotic-behavior-9786202431774","provider":"Atlantic Books","version":"1.0","type":"link"}