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On exact solutions to the gas filtration problem in a thin poroelastic layer

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Analytical Methods in Differential Equations
This chapter is in the book Analytical Methods in Differential Equations

Abstract

We prove the solvability of the initial boundary-value problem for the system of equations of two-dimensional unsteady motion of a fluid in a viscoelastic porous medium and construct some exact solutions for this problem.

Abstract

We prove the solvability of the initial boundary-value problem for the system of equations of two-dimensional unsteady motion of a fluid in a viscoelastic porous medium and construct some exact solutions for this problem.

Chapters in this book

  1. Frontmatter I
  2. Preface V
  3. Contents VII
  4. A novel approximate analytical approach for the treatment of delay differential equations with fractional Caputo–Fabrizio derivative and application to an economic model 1
  5. Lie equivalence transformations and differential invariants for a generalized third-order Schrödinger partial differential equation with variable coefficients using real decomposition 13
  6. The existence of solitons in a freely interacting transonic viscous flow 23
  7. Integration by quadratures of Lie(–Hamilton) systems 29
  8. Integration of first-order ODEs by Jacobi fields 41
  9. On the modeling of curvilinear trajectories in inhomogeneous media 51
  10. On the Hamiltonian approach to delay ODEs 67
  11. Some properties of integrable Hamiltonian systems 79
  12. On the numerical and analytical solution of the Cauchy problem for ideal plasticity 89
  13. Using conservation laws for solving boundary value problems in deformable solid mechanics 95
  14. Symmetries of the extended Bogoyavlenskii generalized breaking soliton equation 103
  15. On the instability for one subclass of three-dimensional dynamic equilibrium states of the electron Vlasov–Poisson gas 111
  16. On the instability for one partial class of three-dimensional dynamic equilibrium states of the hydrogen Vlasov–Poisson plasma 121
  17. Exact solutions and automorphic systems of the geopotential forecast equation 131
  18. Application of the equivalence group for constructing invariant solutions of the inhomogeneous Boltzmann equations for a binary mixture of gases 141
  19. Stability of solutions of ordinary differential equations with control and perturbing actions under structural perturbations 153
  20. Regularizing factors for the Euler–Poisson equations 163
  21. The spectrum of a problem on the flow of a polymeric viscoelastic fluid in a cylindrical channel described by Vinogradov–Pokrovski model 173
  22. On exact solutions to the gas filtration problem in a thin poroelastic layer 183
  23. Lie symmetries, conservation laws, optimal system, and exact solutions of a (2+1)-dimensional time fractional parabolic equation 195
https://doi.org/10.1515/9783111570518-019

Chapters in this book

  1. Frontmatter I
  2. Preface V
  3. Contents VII
  4. A novel approximate analytical approach for the treatment of delay differential equations with fractional Caputo–Fabrizio derivative and application to an economic model 1
  5. Lie equivalence transformations and differential invariants for a generalized third-order Schrödinger partial differential equation with variable coefficients using real decomposition 13
  6. The existence of solitons in a freely interacting transonic viscous flow 23
  7. Integration by quadratures of Lie(–Hamilton) systems 29
  8. Integration of first-order ODEs by Jacobi fields 41
  9. On the modeling of curvilinear trajectories in inhomogeneous media 51
  10. On the Hamiltonian approach to delay ODEs 67
  11. Some properties of integrable Hamiltonian systems 79
  12. On the numerical and analytical solution of the Cauchy problem for ideal plasticity 89
  13. Using conservation laws for solving boundary value problems in deformable solid mechanics 95
  14. Symmetries of the extended Bogoyavlenskii generalized breaking soliton equation 103
  15. On the instability for one subclass of three-dimensional dynamic equilibrium states of the electron Vlasov–Poisson gas 111
  16. On the instability for one partial class of three-dimensional dynamic equilibrium states of the hydrogen Vlasov–Poisson plasma 121
  17. Exact solutions and automorphic systems of the geopotential forecast equation 131
  18. Application of the equivalence group for constructing invariant solutions of the inhomogeneous Boltzmann equations for a binary mixture of gases 141
  19. Stability of solutions of ordinary differential equations with control and perturbing actions under structural perturbations 153
  20. Regularizing factors for the Euler–Poisson equations 163
  21. The spectrum of a problem on the flow of a polymeric viscoelastic fluid in a cylindrical channel described by Vinogradov–Pokrovski model 173
  22. On exact solutions to the gas filtration problem in a thin poroelastic layer 183
  23. Lie symmetries, conservation laws, optimal system, and exact solutions of a (2+1)-dimensional time fractional parabolic equation 195
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