Linear vs. nonlinear selection for the propagation speed of the solutions of scalar reaction‐diffusion equations invading an unstable equilibrium
暂无分享,去创建一个
[1] C. Muratov. A global variational structure and propagation of disturbances in reaction-diffusion systems of gradient type , 2004 .
[2] W. Saarloos. Front propagation into unstable states , 2003, cond-mat/0308540.
[3] P. Holmes,et al. Travelling wave solutions of the degenerate Kolmogorov–Petrovski–Piskunov equation , 2003, European Journal of Applied Mathematics.
[4] J. Billingham. Phase plane analysis of one-dimensional reaction diffusion waves with degenerate reaction terms , 2000 .
[5] A. Merzhanov,et al. Physics of reaction waves , 1999 .
[6] R. Benguria,et al. Speed of Fronts of the Reaction-Diffusion Equation. , 1995, Physical review letters.
[7] Vitaly Volpert,et al. Traveling Wave Solutions of Parabolic Systems , 1994 .
[8] R. Benguria,et al. Validity of the linear speed selection mechanism for fronts of the nonlinear diffusion equation. , 1994, Physical review letters.
[9] M. Cross,et al. Pattern formation outside of equilibrium , 1993 .
[10] Henri Berestycki,et al. Travelling fronts in cylinders , 1992 .
[11] A. Newell,et al. Competition between generic and nongeneric fronts in envelope equations. , 1991, Physical review. A, Atomic, molecular, and optical physics.
[12] W vanSaarloos,et al. Front Propagation into Unstable States II : Linear versus Nonlinear Marginal Stability and Rate of Convergence , 1989 .
[13] Eshel Ben-Jacob,et al. Pattern propagation in nonlinear dissipative systems , 1985 .
[14] R. J. Field,et al. Oscillations and Traveling Waves in Chemical Systems , 1985 .
[15] Pierre-Louis Lions,et al. Nonlinear scalar field equations, I existence of a ground state , 1983 .
[16] F. Rothe,et al. Convergence to pushed fronts , 1981 .
[17] Paul C. Fife,et al. Mathematical Aspects of Reacting and Diffusing Systems , 1979 .
[18] D. Aronson,et al. Multidimensional nonlinear di u-sion arising in population genetics , 1978 .
[19] K. P. Hadeler,et al. Travelling fronts in nonlinear diffusion equations , 1975 .
[20] R. Fisher. THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES , 1937 .
[21] C. Muratov,et al. Existence of traveling wave solutions for Ginzburg-Landau-type problems in infinite cylinder , 2004 .
[22] E. Cheney. Analysis for Applied Mathematics , 2001 .
[23] J. Roquejoffre. Eventual monotonicity and convergence to travelling fronts for the solutions of parabolic equations in cylinders , 1997 .
[24] P. Bassanini,et al. Elliptic Partial Differential Equations of Second Order , 1997 .
[25] G. D. Maso,et al. An Introduction to-convergence , 1993 .
[26] van Saarloos W. Front propagation into unstable states. II. Linear versus nonlinear marginal stability and rate of convergence. , 1989, Physical review. A, General physics.
[27] A. Kolmogoroff,et al. Study of the Diffusion Equation with Growth of the Quantity of Matter and its Application to a Biology Problem , 1988 .
[28] W. van Saarloos,et al. Front propagation into unstable states: Marginal stability as a dynamical mechanism for velocity selection. , 1988, Physical review. A, General physics.
[29] D. Aronson,et al. Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation , 1975 .