Geodesic
Critical Exponents for Nondiagonal Quasilinear Parabolic Systems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Studies on function theory and differential equations, Tome 248 (2005), pp. 46-51 
K. O. Besov. Critical Exponents for Nondiagonal Quasilinear Parabolic Systems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Studies on function theory and differential equations, Tome 248 (2005), pp. 46-51. http://geodesic.mathdoc.fr/item/TM_2005_248_a4/
@article{TM_2005_248_a4,
     author = {K. O. Besov},
     title = {Critical {Exponents} for {Nondiagonal} {Quasilinear} {Parabolic} {Systems}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {46--51},
     year = {2005},
     volume = {248},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2005_248_a4/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Using the method of nonlinear capacity (integral relations), critical exponents for the nonexistence of nontrivial nonnegative solutions are found for the Cauchy problem for systems of inequalities of the form $(u_i)_t-\operatorname {div} A_i(t,x,u_i,\nabla u_i)\ge b_i\prod _{j=1}^2 u_j^{Q_{ij}}+f_i$, where $Q_{ij}\ge 0$, $u_i=u_i(t,x)\ge 0$, $b_i=b_i(t,x)\ge 0$, and $f_i=f_i(t,x)\ge 0$, $x\in \mathbb R^N$, $t\ge 0$. Under additional assumptions concerning the functions $A_i$, a priori estimates and estimates of the lifespan of solutions are obtained in terms of the behavior of initial data and the functions $f_i$.

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