Wyniki wyszukiwania:

The existence and qualitative properties of nontrivial solutions for some important nonlinear Schr dinger systems have been studied in this thesis. For a well-known system arising from nonlinear optics and Bose-Einstein condensates (BEC), in the subcritical case, qualitative properties of ground state solutions, including an optimal parameter range for the existence, the uniqueness and asymptotic behaviors, have been investigated and the results could firstly partially answer open questions raised by Ambrosetti, Colorado and Sirakov. In the critical case, a systematical research on ground...

The existence and qualitative properties of nontrivial solutions for some important nonlinear Schr dinger systems have been studied in this thesis. For a well-known system arising from nonlinear optics and Bose-Einstein condensates (BEC), in the subcritical case, qualitative properties of ground state solutions, including an optimal parameter range for the existence, the uniqueness and asymptotic behaviors, have been investigated and the results could firstly partially answer open questions raised by Ambrosetti, Colorado and Sirakov. In the critical case, a systematical research on ground...

This open access book provides a comprehensive overview of the author’s in-depth insights into the theory, prediction methods, and developmental trends of creep instability and failure in coal-rock masses within mining stopes. The content primarily covers topics such as creep instability of coal-rock masses in stopes, creep instability of surrounding rock in roadways, large-scale roof creep instability, creep instability of...

This open access book presents the Coal remains the primary energy source in China, with an estimated total coal reserve of 59 trillion tons at depths of less than 2000 meters. Among these, over 50% lie at depths exceeding 1000 meters, primarily distributed in central and eastern China. Deep coal mining has become the new norm for the coal industry’s development and resource exploitation. To ensure energy supply for the rapid economic development of central and eastern regions, mining coal resources from depths of over 1000 meters is inevitable. This endeavor holds...

Spontaneous potential (SP) well-logging is one of the most common and useful well-logging techniques in petroleum exploitation. This monograph is the first of its kind on the mathematical model of spontaneous potential well-logging and its numerical solutions. The mathematical model established in this book shows the necessity of introducing Sobolev spaces with fractional power, which seriously increases the difficulty of proving the well-posedness and proposing numerical solution schemes. In this book, in the axisymmetric situation the well-posedness of the corresponding mathematical...