# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Global existence and nonexistence theorems for quasilinear evolution equations of formally parabolic type. (English) Zbl 0891.35062
The authors study global existence and nonexistence of solutions of abstract quasilinear evolution problems involving potential operators. Using energy methods, they show nonexistence of global solutions provided the energy of the initial function is negative (or $\ll 0$). The global existence result is based on suitable structure conditions on the corresponding potentials. The abstract theory is illustrated by examples of the type $|{u}_{t}{|}^{m-2}{u}_{t}-a\nabla ·{\left(|\nabla u|}^{q-2}{\nabla u\right)=|u|}^{p-2}u$.

##### MSC:
 35K60 Nonlinear initial value problems for linear parabolic equations 35K65 Parabolic equations of degenerate type 35B40 Asymptotic behavior of solutions of PDE