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Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which enrich the theory of partial differential equations. This book provides a comprehensive presentation...
Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which enrich the theory of partial differential equations.This book provides a comprehensive presentation of the basic problems, main results and typical methods for nonlinear diffusion equations with degeneracy. Some results for equations with singularity are touched upon.
After dying from a strange terminal illness, Ling Lan was reborn into a world 10000 years into the future. Although she dearly wished she could just live a peaceful and uneventful life in her new healthy body, fate had other plans ... Forced to disguise herself as a boy just so she could inherit her deceased father's premium military benefits, Ling Lan's journey to adulthood was full of challenges. After much difficulty, she finally turned sixteen when she could drop the charade. But before she could grasp her newfound freedom to get married and start her own family, a twist of fate results in her being thrown into the Federation's top military boys' school. With these twists of fate, Ling Lan had little choice but to walk further and further down a path of no return, one of cold and aloof dominance ...
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His will is tough and he is unwilling to be normal. However, his pathway was destined to be that way, being born in a small sect¡¯s branch. However, one day, his left eye merges with the eye of an Ancient God in an accident. From that moment on, he turns from a fish into a dragon. He rises up like a star, walking the path of a legendary cultivator. From being a tiny, small ant at the bottom of the world, he rises step by step, into a place full of powerful sects, strong ancient clans and countless geniuses. This is an era of legends.
This book presents recent results concerning the global existence in time, the large-time behavior, decays of solutions and the existence of global attractors for nonlinear parabolic-hyperbolic coupled systems of evolutionary partial differential equations.
This book presents recent results on nonlinear evolutionary fluid equations such as the compressible (radiative) magnetohydrodynamics (MHD) equations, compressible viscous micropolar fluid equations, the full non-Newtonian fluid equations and non-autonomous compressible Navier-Stokes equations. These types of partial differential equations arise in many fields of mathematics, but also in other branches of science such as physics and fluid dynamics. This book will be a valuable resource for graduate students and researchers interested in partial differential equations, and will also benefit practitioners in physics and engineering.
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