NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

MAT4PDE

2021

Credit points: 15

Subject outline

Many quantities of practical interest in continuum mechanics, environmental mechanics and population ecology, are commonly represented as smooth functions of space and time that are governed by nonlinear partial differential equations. Such equations arise also in differential geometry of smooth manifolds. Some understanding of nonlinear partial differential equations is considered to be essential for any further development of applicable analysis or continuum geometry, with impacts on many other branches of mathematics, physics, chemistry, finance and biology. Topics covered include (i) local formulation of conservation laws, (ii) classical and weak solutions of hyperbolic, parabolic and elliptic equations, (iii) method of characteristics (iv) viscosity solutions of Burgers' equation, (v) reversible and irreversible processes, (vi) integrable nonlinear diffusion equations, (vii) curvature-driven flows, (viii) reaction-diffusion equations and (ix) solitons.

SchoolEngineering and Mathematical Sciences

Credit points15

Subject Co-ordinatorLuke Prendergast

Available to Study Abroad/Exchange StudentsYes

Subject year levelYear Level 4 - UG/Hons/1st Yr PG

Available as ElectiveNo

Learning ActivitiesN/A

Capstone subjectNo

Subject particulars

Subject rules

Prerequisites MAT2VCA and 30 credit points of 3rd year Mathematics subjects (MAT3 or STM3)

Co-requisitesN/A

Incompatible subjectsN/A

Equivalent subjectsN/A

Quota Management StrategyN/A

Quota-conditions or rulesN/A

Special conditionsN/A

Minimum credit point requirementN/A

Assumed knowledgeN/A

Career Ready

Career-focusedNo

Work-based learningNo

Self sourced or Uni sourcedN/A

Entire subject or partial subjectN/A

Total hours/days requiredN/A

Location of WBL activity (region)N/A

WBL addtional requirementsN/A

Graduate capabilities & intended learning outcomes

Graduate Capabilities

Intended Learning Outcomes

01. Demonstrate method of characteristics for solving first-order and second-order nonlinear wave equations.
02. Solve Burgers' equation with standard boundary conditions, relate these to the travelling wave solution and the viscosity solution of inviscid Burgers' equation
03. Construct entropy measures for nonlinear diffusion equations.
04. Solve nonlinear boundary value problems for diffusion equations.
05. Distinguish nonlinear dynamical behaviour from linear dynamical behaviour.
06. Recognise the role of women and various cultures in the science of nonlinear partial differential equations.

Subject options

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Start date between: and    Key dates

Melbourne (Bundoora), 2021, Semester 1, Day

Overview

Online enrolmentNo

Maximum enrolment sizeN/A

Subject Instance Co-ordinatorLuke Prendergast

Class requirements

LectureWeek: 10 - 22
Two 1.00 h lecture per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.

Assessments

Assessment elementCommentsCategoryContributionHurdle% ILO*
2-hour exam (approx. 3000 words) Alternative weightings for assessment items may be negotiated with the subject coordinator.N/AN/AN/ANo50 SILO1, SILO2, SILO3, SILO4
2 assignments (approx. 750 words each)N/AN/AN/ANo30 SILO1, SILO2, SILO3, SILO4, SILO5
3rd assignment (approx. 750 words)N/AN/AN/ANo10 SILO1, SILO2, SILO3, SILO4, SILO5
15 min seminar (equivalent to 750 words)N/AN/AN/ANo10 SILO5, SILO6