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Preface; Contents; Part I Theory and Applications of Mathematical Models in Physical and Chemical Sciences; Compressibility Coefficients in Nonlinear Transport Models in Unconventional Gas Reservoirs; 1 Introduction; 2 Physical Properties of Shale Gas Reservoirs; 3 Mathematical Formulation; 4 Model Validation Under Steady State Conditions; 5 Sensitivity Analysis and Estimation of Model Parameters; 6 Summary; References; Solutions of Time-Fractional Diffusion Equation with Reflecting and Absorbing Boundary Conditions Using Matlab; 1 Introduction
2 Fundamental Solution of Time Fractional Diffusion Equation3 Numerical Solutions; 3.1 Discretization of Boundary Conditions; 4 Matlab Codes; 5 Numerical Experiments; 6 Conclusions; References; Homoclinic Structure for a Generalized Davey-Stewartson System; 1 Introduction; 2 Linearized Stability Analysis; 3 Homoclinic Structure of the GDS System; 4 Conclusions; References; Numerical Simulations of the Dynamics of Vortex Rossby Waves on a Beta-Plane; 1 Introduction; 2 Configuration and Equations; 3 Results; 4 Concluding Remarks; References
On the Problem of Similar Motions of a Chain of Coupled Heavy Rigid Bodies1 Introduction; 2 Description of the Model; 3 Formulation of the Problem; 4 Structure of the Solution; 5 On Compatibility of the Conditions (9) and (16); 6 Geometry of the Motion of the Chain's Skeleton ; References; On Stabilization of an Unbalanced Lagrange Gyrostat; 1 Introduction; 2 Description of the Model; 3 The Problem of Interest; 4 Analysis of Necessary Stability Conditions; 5 Conclusion; Appendix; References; Approximate Solution of Some Boundary Value Problems of Coupled Thermo-Elasticity; 1 Introduction
2 Fundamental and Singular Solutions3 Approximate Solutions; 4 Conclusion; References; Symmetry-Breaking Bifurcations in Laser Systems with All-to-All Coupling; 1 Introduction; 2 Laser Systems with All-to-All Coupling; 3 Symmetric CLMs; 4 Symmetry-Breaking Bifurcations; 5 Conclusion; References; Effect of Jet Impingement on Nano-aerosol Soot Formation in a Paraffin-Oil Flame; 1 Introduction; 2 The Governing Equations; 3 Computational Method; 4 The Benchmark Test Case and Validation; 5 The Results and Discussion; 6 Conclusion; References
Normalization of Eigenvectors and Certain Properties of Parameter Matrices Associated with The Inverse Problem for Vibrating Systems1 Introduction; 2 Preliminaries; 3 Eigenvector Normalization; 4 Consequences of Normalization; References; Computational Aspects of Solving Inverse Problems for Elliptic PDEs on Perforated Domains Using the Collage Method; 1 Introduction; 2 The Collage Theorem for Elliptic PDEs; 3 Theoretical Results; 4 Examples; References; Dynamic Boundary Stabilization of a Schrödinger Equation Through a Kelvin-Voigt Damped Wave Equation; 1 Introduction
2 Fundamental Solution of Time Fractional Diffusion Equation3 Numerical Solutions; 3.1 Discretization of Boundary Conditions; 4 Matlab Codes; 5 Numerical Experiments; 6 Conclusions; References; Homoclinic Structure for a Generalized Davey-Stewartson System; 1 Introduction; 2 Linearized Stability Analysis; 3 Homoclinic Structure of the GDS System; 4 Conclusions; References; Numerical Simulations of the Dynamics of Vortex Rossby Waves on a Beta-Plane; 1 Introduction; 2 Configuration and Equations; 3 Results; 4 Concluding Remarks; References
On the Problem of Similar Motions of a Chain of Coupled Heavy Rigid Bodies1 Introduction; 2 Description of the Model; 3 Formulation of the Problem; 4 Structure of the Solution; 5 On Compatibility of the Conditions (9) and (16); 6 Geometry of the Motion of the Chain's Skeleton ; References; On Stabilization of an Unbalanced Lagrange Gyrostat; 1 Introduction; 2 Description of the Model; 3 The Problem of Interest; 4 Analysis of Necessary Stability Conditions; 5 Conclusion; Appendix; References; Approximate Solution of Some Boundary Value Problems of Coupled Thermo-Elasticity; 1 Introduction
2 Fundamental and Singular Solutions3 Approximate Solutions; 4 Conclusion; References; Symmetry-Breaking Bifurcations in Laser Systems with All-to-All Coupling; 1 Introduction; 2 Laser Systems with All-to-All Coupling; 3 Symmetric CLMs; 4 Symmetry-Breaking Bifurcations; 5 Conclusion; References; Effect of Jet Impingement on Nano-aerosol Soot Formation in a Paraffin-Oil Flame; 1 Introduction; 2 The Governing Equations; 3 Computational Method; 4 The Benchmark Test Case and Validation; 5 The Results and Discussion; 6 Conclusion; References
Normalization of Eigenvectors and Certain Properties of Parameter Matrices Associated with The Inverse Problem for Vibrating Systems1 Introduction; 2 Preliminaries; 3 Eigenvector Normalization; 4 Consequences of Normalization; References; Computational Aspects of Solving Inverse Problems for Elliptic PDEs on Perforated Domains Using the Collage Method; 1 Introduction; 2 The Collage Theorem for Elliptic PDEs; 3 Theoretical Results; 4 Examples; References; Dynamic Boundary Stabilization of a Schrödinger Equation Through a Kelvin-Voigt Damped Wave Equation; 1 Introduction