## Differential Equations and Dynamical SystemsDifferential Equations and Dynamical Systems in fifteen chapters from eminent researchers working in the area of differential equations and dynamical systems covers wavelets and their applications, Markovian structural perturbations, conservation laws and their applications, retarded functional differential equations and applications to problems in population dynamics, finite element method and its application to extended Fisher-Kolmogorv equation, generalized K-dV equation, Faedo-Galerkin approximations of solutions to evolution equations, the method of semidiscretization in time and its applications to nonlinear evolution equations, spectral methods, Tikhonov regularization of partial differential equations, mathematical modeling and second order evolution equations. |

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### Contents

Wavelets and Some Applications | 1 |

Trends in Wavelet Methods for Two Point Boundary Value Prob | 15 |

Stability and Convergence of LargeScale Stochastic Approxima | 25 |

Global Correctness Classes of Functional Solutions for Conserva | 49 |

A Nonlinear GasLiquid System in Sliding Motion | 69 |

On Certain Exact Solutions of a Generalized KdVBurger Type | 91 |

Method of Semidiscretization in Time to Nonlinear Retarded Dif | 107 |

Retarded Differential Equations with Applications to Population | 119 |

Spectral Methods as LeastSquares Problems | 127 |

Finite Element Method for Extended FisherKolmogorov EFK | 149 |

Spectral Regularization of a Singularly Perturbed Elliptic Partial | 169 |

Second Order Semilinear Evolution Equations | 179 |

Model for the Effect of Degrading Habitat on the Persistence | 205 |

Schwarzian Derivative of Critically Finite Meromorphic Functions | 213 |

### Common terms and phrases

algorithm Anal analysis Appl applications approximate integral equations assumptions Bahuguna Banach space boundary value problems bounded Cauchy problem coefficients compact set comparison theorems completes the proof Comput consider convergence Daubechies defined definition denote Department of Mathematics dimensional dip tube discontinuity dynamics estimates existence and uniqueness Faedo-Galerkin approximations functional solution G D(A Galerkin method global habitat Hence Hilbert space Hq(I inequality initial boundary value initial data integral equations interval of existence Kanpur Lemma linear operator Lipschitz continuous liquid model Math matrix maximal interval meromorphic function Moudgalya nonlinear obtain ordinary differential equations orthogonal parameter Pazy perturbed polynomial regularization methods satisfies scaling function Schwarzian derivative semigroup semilinear sliding motion smooth solution process solution to 1.2 Spectral methods stability stochastic stochastic approximation theory Tikhonov Tikhonov regularization tmax topology vector wavelets zero