Solvability for a New Class of Moore-Gibson-Thompson Equation with Viscoelastic Memory, Source Terms, and Integral Condition

This paper deals with the existence and uniqueness of solutions of a new class of Moore-Gibson-Thompson equation with respect to the nonlocal mixed boundary value problem, source term, and nonnegative memory kernel. Galerkin’s method was the main used tool for proving our result. This work is a generalization of recent homogenous work.

[1]  R. Triggiani,et al.  An abstract semigroup approach to the third‐order Moore–Gibson–Thompson partial differential equation arising in high‐intensity ultrasound: structural decomposition, spectral analysis, exponential stability , 2012 .

[2]  S. Boulaaras,et al.  Galerkin method for nonlocal mixed boundary value problem for the Moore‐Gibson‐Thompson equation with integral condition , 2019, Mathematical Methods in the Applied Sciences.

[3]  Salah Boulaaras,et al.  A new proof for the existence and uniqueness of the discrete evolutionary HJB equations , 2015, Appl. Math. Comput..

[4]  Richard E. Ewing,et al.  A class of parameter estimation techniques for fluid flow in porous media , 1991 .

[5]  Stokes.  XXXVIII. An examination of the possible effect of the radiation of heat on the propagation of sound , 1851 .

[6]  Oleg A. Sapozhnikov,et al.  Nonlinear Wave Processes in Acoustics , 1998 .

[7]  S. Boulaaras.  SOLVABILITY OF THE MOORE–GIBSON–THOMPSON EQUATION WITH VISCOELASTIC MEMORY TERM AND INTEGRAL CONDITION VIA GALERKIN METHOD , 2021 .

[8]  R. Agarwal,et al.  On the continuation principle of local smooth solution for the Hall-MHD equations , 2020, Applicable Analysis.

[9]  S. Boulaaras.  Some new properties of asynchronous algorithms of theta scheme combined with finite elements methods for an evolutionary implicit 2‐sided obstacle problem , 2017 .

[10]  R. Agarwal,et al.  A regularity criterion of the 3D MHD equations involving one velocity and one current density component in Lorentz space , 2020, Zeitschrift für angewandte Mathematik und Physik.

[11]  Y. Choi,et al.  A parabolic equation with nonlocal boundary conditions arising from electrochemistry , 1992 .

[12]  J. R. Cannon,et al.  The solution of the heat equation subject to the specification of energy , 1963 .

[13]  Karl Kunisch,et al.  A reaction-diffusion system arising in modelling man-environment diseases , 1988 .

[14]  Salah Boulaaras,et al.  L∞-asymptotic behavior for a finite element approximation in parabolic quasi-variational inequalities related to impulse control problem , 2011, Appl. Math. Comput..

[15]  P. Jordan.  Second-sound phenomena in inviscid, thermally relaxing gases , 2014 .

[16]  Ravi P. Agarwal,et al.  A Regularity Criterion in Weak Spaces to Boussinesq Equations , 2020, Mathematics.

[17]  O. A. Ladyzhenskai︠a︡.  Boundary value problems of mathematical physics , 1967 .

[18]  S. Gala,et al.  A regularity criterion for local strong solutions to the 3D Stokes-MHD equations , 2020 .

[19]  J. Henderson,et al.  POSITIVE SOLUTIONS OF A NONLINEAR HIGHER ORDER BOUNDARY-VALUE PROBLEM , 2009 .

[20]  S. Mesloub,et al.  On the higher dimension Boussinesq equation with nonclassical condition , 2011 .

[21]  I. Lasiecka,et al.  Moore-Gibson-Thompson equation with memory, part II: general decay of energy , 2015, 1505.07525.

[22]  L. S. Pul’kina.  A non-local problem with integral conditions for hyperbolic equations. , 1999 .

[23]  Baruch Cahlon,et al.  Stepwise stability for the heat equation with a nonlocal constraint , 1995 .

[24]  B. Kaltenbacher,et al.  WELL-POSEDNESS AND EXPONENTIAL DECAY OF THE ENERGY IN THE NONLINEAR JORDAN–MOORE–GIBSON–THOMPSON EQUATION ARISING IN HIGH INTENSITY ULTRASOUND , 2012 .

[25]  I. Lasiecka,et al.  Moore–Gibson–Thompson equation with memory, part I: exponential decay of energy , 2015, 1505.07523.

[26]  S. Mesloub.  A nonlinear nonlocal mixed problem for a second order pseudoparabolic equation , 2006 .

[27]  G. Lebon,et al.  Propagation of Ultrasonic Sound-waves in Dissipative Dilute Gases and Extended Irreversible Thermodynamics , 1989 .

[28]  M. Théra,et al.  On the Regularity of Weak Solutions of the Boussinesq Equations in Besov Spaces , 2020, Vietnam Journal of Mathematics.