Parabolik-Eliptik Doğrusal Olmayan Sistemler İçin Çözümlerin Varlığı ve Düzenliliği

Özet (abstract)

Abstract In this paper, we study the existence and summability of the solutions to the following parabolic–elliptic system of partial differential equations with discontinuous coefficients: $$\begin{aligned} \left\{ \begin{array}{cc} u_t-\operatorname {div}(A(x, t) \nabla u)=-\operatorname {div}(u M(x) \nabla \psi )+f(x,t) & \text { in } \Omega _T, \\ -\operatorname {div}(M(x) \nabla \psi )=|u|^\theta & \text { in } \Omega _T, \\ \psi (x, t)=0 & \text { on } \partial \Omega \times (0, T), \\ u(x, t)=0 & \text { on } \partial \Omega \times (0, T), \\ u(x, 0)=0 & \text { in } \Omega \end{array}\right. \end{aligned}$$ u t - div ( A ( x , t ) ∇ u ) = - div ( u M ( x ) ∇ ψ ) + f ( x , t ) in Ω T , - div ( M ( x ) ∇ ψ ) = | u | θ in Ω T , ψ ( x , t ) = 0 on ∂ Ω × ( 0 , T ) , u (

Yazarların özeti; kaynağından alınmıştır. Journal of Evolution Equations, 2026 · DOI ↗