This course gives lecture on mathematical analysis for hyperbolic systems of balance laws. We develope the general mathematical theory on the global existence and asymptotic stability of solutions.
The aim of this course is as follows. We treat hyperbolic systems of balance laws as nonlinear partial differential equations. We formulate structural conditions on the system and under these structural conditions, we prove the global existence and asymptotic stability of solutions for small initial data. The proof is based on the energy method and the semigroup technique.
・To understand the physical and mathematical meaning of the structural conditions
・To understand the dissipative structure of the system
・To learn the energy method
・To learn the semigroup technique
・To understand the mathematical theory on the global existence and asymptotic stability of solutions
hyperbolic system of balance laws, mathematical entropy, symmetrization of system, stability condition, craftsmanship condition, dissipative structure, decay property, global solution, energy method, a priori estimate, asymptotic stability, semigroup technique
|Intercultural skills||Communication skills||✔ Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
This is a standard lecture course. There will be some assignments.
|Course schedule||Required learning|
|Class 1||・Introduction (Hyperbolic system of balance laws) ・Mathematical entropy and symmetrization ・Decay property for linearized system ・Dissipative structure ・Results on the global existence ・Energy estimates (A priori estimates) ・Time-weighted energy estimates ・Decay estimates||Details will be provided during each class session|
Reference texts will be given during the class.
Students are expected to have passed Differential Equations I and Differential Equations II.