New instability, blow-up and break-down effects for Sobolev-type evolution PDE: asymptotic analysis for a celebrated pseudo-parabolic model on the quarter-plane

DOI10.1007/s42985-024-00296-wMaRDI QIDQ6645960

Tohru Ozawa, Unnamed Author

Publication date: 29 November 2024

Published in: SN Partial Differential Equations and Applications (Search for Journal in Brave)

zbMATH Keywords

mathematical physicsrigorous analysissecond-order fluidstwo-temperature heat conductionSobolev-type evolution equationsnonhomogeneous initial-boundary-value problems on the quarter-planeinstability effectsBarenblatt pseudo-parabolic modeldiffusion of radiationintegral representations in the spectral Fourier planerational dispersion relationRobin dataseepage in porous solidsspatiotemporal asymptoticsunified-transform method

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics (74H10) Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Flows in porous media; filtration; seepage (76S05) Asymptotic methods, singular perturbations applied to problems in fluid mechanics (76M45) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Integral representations of solutions to PDEs (35C15) Asymptotic expansions of solutions to PDEs (35C20) Ultraparabolic equations, pseudoparabolic equations, etc. (35K70) Radiative transfer in astronomy and astrophysics (85A25) Asymptotic analysis for problems in thermodynamics and heat transfer (80M35) Initial-boundary value problems for linear higher-order PDEs (35G16) PDEs in connection with classical thermodynamics and heat transfer (35Q79) Complex-variable methods applied to problems in solid mechanics (74S70) Diffusive and convective heat and mass transfer, heat flow (80A19) PDEs in connection with semiconductor devices (35Q81)

Cites Work

• Large-time asymptotic behaviour of solutions of non-linear Sobolev-type equations
• Homogenization of a pseudoparabolic system
• Lax pairs: a novel type of separability
• Unsteady flow of a second-order fluid between concentric cylinders
• A Nonlinear Pseudoparabolic Diffusion Equation
• Fourier Spectral Methods for Pseudoparabolic Equations
• Existence and uniqueness in nonclassical diffusion
• The Uniqueness Class for the Cauchy Problem for Pseudoparabolic Equations
• ON THE THEORY OF DIFFUSION IN MEDIA WITH DOUBLE DIFFUSIVITY I. BASIC MATHEMATICAL RESULTS
• ON THE THEORY OF DIFFUSION IN MEDIA WITH DOUBLE DIFFUSIVITY II. BOUNDARY-VALUE PROBLEMS
• Controllability Properties of Pseudo-Parabolic Boundary Control Problems
• Implicit Degenerate Evolution Equations and Applications
• A pseudo-parabolic variational inequality and Stefan problem
• Stable Patterns in a Viscous Diffusion Equation
• Initial boundary value problem for nonlinear pseudoparabolic equations
• The Approximation of Certain Parabolic Equations Backward in Time by Sobolev Equations
• Approximate equations for long water waves
• On the analytic theory of Pseudoparabolic systems
• A Runge Approximation and Unique Continuation Theorem for Pseudoparabolic Equations
• A unified transform method for solving linear and certain nonlinear PDEs
• Identification problems for pseudoparabolic integrodifferential operator equations
• Mathematical model of the non equilibrium water oil displacement in porous strata
• A new transform method for evolution partial differential equations
• An integrable shallow water equation with peaked solitons
• Infiltration in porous media with dynamic capillary pressure: travelling waves
• Fokas’s Unified Transform Method for linear systems
• A numerical implementation of the unified Fokas transform for evolution problems on a finite interval
• Initial-boundary value problems of the coupled modified Korteweg–de Vries equation on the half-line via the Fokas method
• Lifespan for a semilinear pseudo‐parabolic equation
• Explicit integral solutions for the plane elastostatic semi-strip
• Local regularity, boundary values and maximum principles for pseudoparabolic equations
• Effect of aggregation on population recovery modeled by a forward-backward pseudoparabolic equation
• ON NON-ALMOST-PERIODICITY OF SOLUTIONS OF THE SOBOLEV PROBLEM IN DOMAINS WITH EDGES
• Non-equilibrium imbibition of a porous block
• Asymptotic expansion of solutions to the periodic problem for a non-linear Sobolev-type equation
• Initial value problem for fractional Volterra integrodifferential pseudo-parabolic equations
• The Neumann and Robin problems for the Korteweg–de Vries equation on the half-line
• The unified transform for evolution equations on the half‐line with time‐periodic boundary conditions*
• The KdV Equation on the Half-Line: Time-Periodicity and Mass Transport
• The Cauchy Problem for One Equation of Sobolev Type
• Unified Transform for Boundary Value Problems
• A hybrid analytical–numerical method for solving evolution partial differential equations. I. The half-line
• A numerical technique for linear elliptic partial differential equations in polygonal domains
• Nonlocal and Multipoint Boundary Value Problems for Linear Evolution Equations
• The Method of Fokas for Solving Linear Partial Differential Equations
• Pseudoparabolic equations with convection
• The Cauchy problem for an equation of Sobolev type with power non-linearity
• Some Qualitative Properties of Solutions to a Pseudoparabolic Equation Modeling Solvent Uptake in Polymeric Solids
• Incompressible Second-Order Fluids
• Integrals of nonlinear equations of evolution and solitary waves
• On half-space solutions of a modified heat equation
• Pseudoparabolic Partial Differential Equations
• Logarithmic Convexity, First Order Differential Inequalities and Some Applications
• Model equations for long waves in nonlinear dispersive systems
• ON THE ANALYTIC THEORY OF PSEUDOPARABOLIC EQUATIONS
• General Boundary Value Problems for Differential Equations of Sobolev Type
• Terminal value problem for nonlinear parabolic and pseudo-parabolic systems
• The nonlinear Schrödinger equation on the half‐line with homogeneous Robin boundary conditions
• Boundary behavior for the heat equation on the half‐line
• Bounds for blow-up solutions of a semilinear pseudo-parabolic equation with a memory term and logarithmic nonlinearity in variable space
• Pseudoparabolic equations with variable exponents and coefficients: blow-up and large time behaviors
• Integral representations for the double-diffusivity system on the half-line
• Boundary behavior of the solution to the linear Korteweg‐De Vries equation on the half line
• On Barenblatt's pseudoparabolic equation with forcing on the half-line via the Fokas method
• Long-range instability of linear evolution PDE on semi-bounded domains via the Fokas method
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical analysis of Fokas' unified method for linear elliptic PDEs
• Sobolev type fractional abstract evolution equations with nonlocal conditions and optimal multi-controls
• Evolution PDEs and augmented eigenfunctions. half-line
• Instability of positive periodic solutions for semilinear pseudo-parabolic equations with logarithmic nonlinearity
• The linear KdV equation with an interface
• Initial-boundary value problems for the general coupled nonlinear Schrödinger equation on the interval via the Fokas method
• Periodic boundary value problem for nonlinear Sobolev-type equations
• Well-posedness of boundary-value problems for the linear Benjamin-Bona-Mahony equation
• Global existence and finite time blow-up for a class of semilinear pseudo-parabolic equations
• Blow-up phenomena for nonlinear pseudo-parabolic equations with gradient term
• Existence results for nonlinear pseudoparabolic problems
• Asymptotic behaviour of solutions to some pseudoparabolic equations
• An approximation theorem for functionals, with applications in continuum mechanics
• Nonlocal boundary problems for a third-order one-dimensional nonlinear pseudoparabolic equation
• Eventual periodicity for the KdV equation on a half-line
• Cauchy problems of pseudo-parabolic equations with inhomogeneous terms
• Global well-posedness for a fourth order pseudo-parabolic equation with memory and source terms
• The generalized Dirichlet-Neumann map for linear elliptic PDEs and its numerical implementation
• Temporal growth and eventual periodicity for dispersive wave equations in a quarter plane
• A Lewy-type reflection principle for pseudoparabolic equations
• On the problem of diffusion in solids
• On the theory of consolidation with double porosity
• The final value problem for evolution equations
• Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade
• A semilinear Sobolev evolution equation in a Banach space
• The Riemann function for the third-order one-dimensional pseudoparabolic equation
• Slow motion of a body in a fluid of second grade
• Initial-boundary value problems for a class of pseudoparabolic equations with integral boundary conditions
• The diffusion of imprisoned radiation through a gas.
• On the equilibrium of the Sun's atmosphere
• Blowup and blowup time for a class of semilinear pseudo-parabolic equations with high initial energy
• Global existence, exponential decay and finite time blow-up of solutions for a class of semilinear pseudo-parabolic equations with conical degeneration
• Asymptotic behavior at infinity of solutions to the nonhomogeneous Sobolev equation
• Bounds for blow-up time in nonlinear pseudo-parabolic equations
• Global existence and blow-up of solutions for infinitely degenerate semilinear pseudo-parabolic equations with logarithmic nonlinearity
• Zero-dispersion limit for integrable equations on the half-line with linearisable data
• Classical and weak solutions for one-dimensional pseudo-parabolic equations with typical boundary data
• Asymptotic behaviour of the solutions of inverse problems for pseudo-parabolic equations
• Some nonexistence and instability theorems for solutions of formally parabolic equations of the form \(Pu_t=-Au+ {\mathfrak F} (u)\)
• A model problem for groundwater flow with dynamic capillary pressure: stability of travelling waves
• An inverse problem for a pseudoparabolic integro-differential operator equation
• Boundary control for a class of pseudo-parabolic differential equations
• On an initial and final value problem for fractional nonclassical diffusion equations of Kirchhoff type
• Analysis of a pseudo-parabolic equation by potential wells
• An inverse problem for the pseudo-parabolic equation with p-Laplacian
• Regularized solution approximation of a fractional pseudo-parabolic problem with a nonlinear source term and random data
• On a pseudo-parabolic equations with a non-local term of the Kirchhoff type with random Gaussian white noise
• The Korteweg-de Vries equation on the half-line with Robin and Neumann data in low regularity spaces
• A higher dispersion KdV equation on the half-line
• Existence and blow-up of weak solutions of a pseudo-parabolic equation with logarithmic nonlinearity
• An elementary proof of the lack of null controllability for the heat equation on the half line
• On a terminal value problem for pseudoparabolic equations involving Riemann-Liouville fractional derivatives
• Global existence and blow up of solutions for pseudo-parabolic equation with singular potential
• Global existence and finite time blowup for a nonlocal semilinear pseudo-parabolic equation
• A vanishing dynamic capillarity limit equation with discontinuous flux
• On a final value problem for a nonlinear fractional pseudo-parabolic equation
• Reconstructing an unknown potential term in the third-order pseudo-parabolic problem
• A cooling process according to two-temperature theory of heat conduction
• Finite time blowup for a semilinear pseudo-parabolic equation with general nonlinearity
• Global solutions and blow up solutions to a class of pseudo-parabolic equations with nonlocal term
• A semilinear pseudo-parabolic equation with initial data non-rarefied at \(\infty\)
• A global existence result for the equations describing unsaturated flow in porous media with dynamic capillary pressure
• Dynamic capillary effects in heterogeneous porous media
• The global existence and time-decay for the solutions of the fractional pseudo-parabolic equation
• A generalized eigenproblem for the Laplacian which arises in lightning
• Certain non-steady flows of second-order fluids
• On a theory of heat conduction involving two temperature
• Parabolic and pseudo-parabolic partial differential equations
• Local regularity of solutions of Sobolev-Galpern partial differential equations
• Pseudoparabolic equations in one space variable
• Asymptotic behavior of solutions of pseudo-parabolic partial differential equations
• Wave propagation in the two temperature theory of thermoelasticity
• Solutions of pseudo-heat equations in the whole space
• A quasilinear parabolic and a related third order problem
• Start-up flows of second grade fluids in domains with one finite dimension
• On the well-posedness of a nonlinear pseudo-parabolic equation
• General decay and blow-up results for a class of nonlinear pseudo-parabolic equations with viscoelastic term
• Regularization of the inverse problem for time fractional pseudo-parabolic equation with non-local in time conditions
• On an initial boundary value problem for fractional pseudo-parabolic equation with conformable derivative
• On the integrability of linear and nonlinear partial differential equations
• The nonlinear Schrödinger equation on the half-line
• On inverse problems for pseudoparabolic and parabolic equations of filtration
• Synthesis, as Opposed to Separation, of Variables
• Nonlinear model of quasi-stationary process in crystalline semiconductor
• A spectral collocation method for the Laplace and modified Helmholtz equations in a convex polygon
• A numerical implementation of Fokas boundary integral approach: Laplace's equation on a polygonal domain
• ON THE EQUATION OF BARENBLATT–SOBOLEV
• A class of pseudo-parabolic equations: existence, uniqueness of weak solutions, and error estimates for the Euler-implicit discretization
• A mathematical model of turbulent heat and mass transfer in stably stratified shear flow
• Nonlinear Degenerate Evolution Equations and Partial Differential Equations of Mixed Type
• Solution of nonlinear pseudoparabolic equations by semidiscretization in time
• Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata]
• A new solution representation for the BBM equation in a quarter plane and the eventual periodicity
• Blow‐up phenomena for a pseudo‐parabolic equation
• A nonlinear pseudoparabolic equation
• A Unified Approach to Boundary Value Problems
• Asymptotics of linear initial boundary value problems with periodic boundary data on the half-line and finite intervals

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