On viscous conservation laws with growing initial data. (English) Zbl 1212.35190

Summary: A local unique solvability is established for viscous conservation laws when the initial data may grow to infinity with a natural order. It is also shown that such a classical solution can be extended to a global-in-time solution provided that the growth order of the initial data is less than the critical order.


35K15 Initial value problems for second-order parabolic equations
35K55 Nonlinear parabolic equations