Conditions for the Existence of Global Solutions to Doubly Nonlinear Advection-diffusion Equations

• Autor(a) principal: CHAGAS,J.Q.
• Data de Publicação: 2020
• Outros Autores: GUIDOLIN,P.L., ZINGANO,P.R.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
• Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512020000100083
• topic: doubly nonlinear parabolic equation; global solutions; conditions for global solutions

ABSTRACT In this work, we consider a initial-value problem for an doubly nonlinear advection-diffusion equation, and we present a critical value of κ up to wich the initial-value problem has global solution independent of the initial data u 0, and from which global solutions may still exists, but from initial data u 0 satisfying certain conditions. For this, we suppose that the function <mml:math><mml:mi mathvariant="bold-italic">f</mml:mi> <mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo> <mml:mi>t</mml:mi><mml:mo>,</mml:mo><mml:mi>u</mml:mi> <mml:mo>)</mml:mo></mml:math> in the advection term, writted in the divergent form, satisfies certain conditions about your variation in ℝ n , and we also use the decrease of the norm L 1 ( ℝ n ) and an control for the norm L ∞ ( ℝ n ) of solution u ( · , t ).