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zennir k p x bi laplacian application time pdes viscoelasticity 2024

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Textbook in PDF format The main subject of our book is to use the (p, p(x) and p(x))-bi-Laplacian operator in some partial differential systems, where we developed and obtained many results in quantitative and qualitative point of view. To our knowledge there are no such references Preface Notations Introduction Spaces and operator settings Energy functional Survey on p(x)-Laplacian operator Viscoelastic materials Viscoelastic term Examples Love-Type Waves with Past History Quantitative studies Existence and uniqueness of local weak solution Global existence of solution via stable set Qualitative studies General decay rate Global nonexistence Viscoelastic Wave Equation with Power Nonlinearity Nonlinearity in polynomial form Stability results of solution to a class of coupled systems with logarithmic nonlinearities Kirchhoff-type equation in viscoelasticity with logarithmic nonlinearity Plate Equation in Rn Cauchy problem for a Petrowsky–Petrowsky system in Rn Polynomial decay rate The lack of exponential decay rate Plate equation with time-varying delay in Rn Nonexistence of Global Solutions for Nonlinear Equation via Contradiction Argument Nonlinear heat equation in bi-Laplacian type Growth with negative initial energy Growth with positive initial energy Blow up at well-defined time for class of wave p(x)-bi-Laplace equation Nonlinear Wave p-Laplace Equation Nonlinear wave equation of φ-Laplacian type Delayed p-Laplace equation p-Laplace equation with nonlinear dissipation in Rn Wave equation involving the fractional p-Laplacian with logarithmic nonlinearity Potential well in a variational stationary setting Local existence of weak solution Global existence of weak solution Nonlinear Kirchhoff-Type Equations with Kelvin–Voigt Damping in Variable Exponents Local existence and global nonexistence Local existence result Global nonexistence of solutions Blow-up of a certain class of solutions p(x)-Laplacian equation with delay term and variable exponents Blow-up using the contradiction argument Decay of solutions Nonlocal Systems Involving the p(x)-Laplacian Operator Positive solutions for nonlocal elliptic systems Nehari manifold approach for fractional p(x)-Laplacian systems Fractional Sobolev spaces with variable exponents Nehari manifold and fibering map analysis Existence of multiple solutions Postlude Sub-Super solution method for nonlocal systems Applications to some nonlocal sublinear problem Concave–convex nonlinearities A generalization of the logistic equation Positive solutions of nonlocal evolutionary systems Dynamics of a Coupled System for Nonlinear Damped Wave Equations with Variable Exponents Energy functional and local solution Global existence and convergence results Lifespan of solutions The case of Ω = Rn Pseudo-Parabolic Equations with p(x) Bi-Laplacian The effect of weak viscoelasticity on the existence of solutions for pseudo-parabolic equations with weak viscoelasticity p(x)-bi-Laplacian pseudo-parabolic equation with memory Bibliography Index

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Zennir K. P(x)-Bi-Laplacian. Application on Time-Pdes in Viscoelasticity 2024.pdf 6.8 MB

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zennir k p x bi laplacian application time pdes viscoelasticity 2024