On the nonexistence of global solutions of the Cauchy problem for the Korteweg-de Vries Equation
We establish conditions on the initial data under which the Cauchy problem for the Korteweg-de Vries equation does not admit a solution global in t > 0. The proof of the results is based on the nonlinear capacity method . In closing, we provide an example.
Key wordsblow-up KdV equation initial-boundary value problem Cauchy problem nonlinear capacity
Unable to display preview. Download preview PDF.
- V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Theory of Solitons: The Inverse Scattering Method, Consultants Bureau (Plenum), New York, 1984.Google Scholar
- E. Mitidieri and S. I. Pokhozhaev, “A priori estimates and blow-up of solutions of nonlinear partial differential equations and inequalities,” Trudy Mat. Inst. Steklov, 234 (2001), 3–383; English transl.: Proc. Steklov Inst. Math., 234 (2001), 1–362.Google Scholar
- S. I. Pokhozhaev, “On a class of initial-boundary value problems for equations of the Korteweg-de Vries type,” Differents. Uravn., 48:3 (2012), 368–374; English transl.: Differ. Equ., 48:3 (2012), 372–378.Google Scholar