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Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations by P.L. Sachdev and Ch. Srinivasa Rao


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Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations written by P.L. Sachdev (Deceased) and Ch. Srinivasa Rao Department of Mathematics, Indian Institute of Technology Madras, Sardar Patel Road, Chennai-600036, India chsrao@iitm.ac.in, drchsrao@yahoo.com . This is an other great mathematics book cover the following topics.

Large Time Asymptotics for Solutions of Nonlinear Partial Differential Equations written by P.L. Sachdev (Deceased) and Ch. Srinivasa Rao cover the following topics.

  • 1 Introduction
    References

  • 2 Large Time Asymptotics for Solutions of Nonlinear First-Order Partial Differential Equations
    2.1 Introduction
    2.2 First-order nonlinear partial differential equations – Some examples
    2.3 Decay estimates for solutions of nonlinear first-order partial differential equations
    2.4 Conclusions
    References

  • 3 Large Time Asymptotic Analysis of Some Nonlinear Parabolic Equations – Some Constructive Approaches
    3.1 Introduction
    3.2 Travelling waves as asymptotics of solutions of initial value problems – The Burgers equation
    3.3 Profile at infinity – Initial boundary value problem for Burgers equation
    3.4 Travelling waves describing flow in a porous medium
    3.5 Evolution of a stable profile describing cross-field diffusion in toroidal multiple plasma
    3.6 Asymptotic solutions describing fast nonlinear diffusion
    3.7 Large time asymptotic behaviour of periodic solutions of some generalised Burgers equations
    3.8 Asymptotic behaviour of some generalised Burgers equations via balancing argument.
    3.9 Evolution of travelling waves in generalised Fisher’s equations via matched asymptotic expansions
    3.10 Periodic travelling wave solutions in reaction–diffusion systems
    3.11 Conclusions
    References

  • 4 Self-similar Solutions as Large Time Asymptotics for Some Nonlinear Parabolic Equations
    4.1 Introduction
    4.2 Self-similar solutions as large time asymptotics for linear heat equation
    4.3 Self-similar solutions as intermediate asymptotics for filtration–absorption model
    4.4 Analysis of a class of similarity solutions of the porous media equation
    4.5 Similarity solutions of nonlinear heat conduction problems as large time asymptotics
    4.6 Large time asymptotics for solutions of the porous media equation
    4.7 Large time behaviour of solutions of a dissipative semilinear heat equation
    4.8 Large time asymptotics for the solutions of a very fast diffusion equation
    4.9 Conclusions
    References.

  • 5 Asymptotics in Fluid Mechanics
    5.1 Introduction...189
    5.2 Strong explosion in a power law density medium – Self-similar solutions of first and second kind....190
    5.3 Self-similar solutions for collapsing cavities...199
    5.4 Large time behaviour of solutions of compressible flow equations with damping..203
    5.5 Large time behaviour of solutions of unsteady boundary layer equations for an incompressible fluid....211
    5.6 Asymptotic behaviour of velocity profiles in Prandtl boundary layer theory.
    5.7 Conclusions

  • References

  • Index

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