Naslov
Estimates on the weak solution of semilinear hyperbolic systems

Autori
Burazin, Krešimir

Izvornik
Annali dell'Università di Ferrara. Sezione 7: Scienze matematiche (0430-3202) 54 (2008), 2; 229-243

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Semilinear hyperbolic systems; Discrete models for Boltzmann’ s equation; Estimates on solution; Time of existence

Sažetak
The Cauchy problem for a semilinear hyperbolic system of the type $$\left\{; ; ; ; \begin{; ; ; ; array}; ; ; ; {; ; ; ; l}; ; ; ; \partial _t {; ; ; ; \sf u}; ; ; ; (t, {; ; ; ; \bf x}; ; ; ; ) +\sum\nolimits_{; ; ; ; k=1}; ; ; ; ^d {; ; ; ; \bf A}; ; ; ; ^k(t, {; ; ; ; \bf x}; ; ; ; )\partial _{; ; ; ; k}; ; ; ; {; ; ; ; \sf u}; ; ; ; (t, {; ; ; ; \bf x}; ; ; ; )={; ; ; ; \sf f}; ; ; ; (t, {; ; ; ; \bf x}; ; ; ; , {; ; ; ; \sf u}; ; ; ; (t, {; ; ; ; \bf x}; ; ; ; ))\\ {; ; ; ; \sf u}; ; ; ; (0, \cdot)={; ; ; ; \sf v}; ; ; ; \end{; ; ; ; array}; ; ; ; \right\}; ; ; ; $$ is considered, with each matrix function A k being diagonal, bounded and locally Lipschitz in x. Discrete models for the Boltzmann equation furnish examples of such systems. For bounded initial data, and right-hand side that is locally Lipschitz and locally bounded in u, local existence and uniqueness results in L∞ are well known, together with some estimates on weak solutions. More precise estimates for weak solutions of the above Cauchy problem will be given, supplemented by estimates on the maximal time of existence for the solution, as well as the local existence and uniqueness in L^p setting (1 < p < ∞ ).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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