The occurrence of collapse for quasilinear equations of parabolic and hyperbolic types

Collapse in finite time is established for part of the solutions of certain classes of quasilinear equations of parabolic and hyperbolic types, the linear part of which has general form. Certain hyperbolic equations having L-M pairs belong to these classes.

[1]  Howard A. Levine,et al.  Some nonexistence and instability theorems for solutions of formally parabolic equations of the form Put=−Au+ℱ(u) , 1973 .

[2]  R. Glassey Blow-up theorems for nonlinear wave equations , 1973 .

[3]  V. Mizel,et al.  Existence and nonexistence in the large of solutions of quasilinear wave equations , 1967 .

[4]  N. Zabusky Exact Solution for the Vibrations of a Nonlinear Continuous Model String , 1962 .

[5]  O. A. Ladyzhenskai︠a︡,et al.  Linear and quasilinear elliptic equations , 1968 .

[6]  D. Sattinger Stability of nonlinear hyperbolic equations , 1968 .

[7]  B. Straughan Further global nonexistence theorems for abstract nonlinear wave equations , 1975 .

[8]  L. Faddeev,et al.  Essentially nonlinear one-dimensional model of classical field theory , 1974 .

[9]  O. Ladyženskaja Linear and Quasilinear Equations of Parabolic Type , 1968 .

[10]  J. Moser Finitely many mass points on the line under the influence of an exponential potential -- an integrable system , 1975 .

[11]  Mark J. Ablowitz,et al.  Method for Solving the Sine-Gordon Equation , 1973 .

[12]  R. Knops,et al.  Non-existence, instability, and growth theorems for solutions of a class of abstract nonlinear equations with applications to nonlinear elastodynamics , 1974 .

[13]  Howard A. Levine,et al.  Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations , 1974 .

[14]  Peter D. Lax,et al.  Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations , 1964 .

[15]  H. Flaschka On the Toda Lattice. II Inverse-Scattering Solution , 1974 .