منابع مشابه
Evolution Equations of Parabolic Type
be linear and quasilinear evolution equations of parabolic type in a Banach space X respectively. By "parabolic type" we mean that A(t) and A(t,u) are all the infinitesimal generators of analytic linear semigroups on X we do not necessarily assume that the domains of the operators A(t) and A("t,u) are dense subspaces of X, so the semigroups generated by them may not be of class c0 J. The domain...
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We adapt the Levi’s parametrix method to prove existence, estimates and qualitative properties of a global fundamental solution to ultraparabolic partial differential equations of Kolmogorov type. Existence and uniqueness results for the Cauchy problem are also proved.
متن کاملPropagation Property for Nonlinear Parabolic Equations of p-Laplacian-Type
We study propagation property for one-dimensional nonlinear diffusion equations with convection-absorption, including the prototype model ∂t(u m)− ∂x(|∂xu|p−1∂xu)− μ|∂xu|q−1∂xu+ λu = 0, where m, p, q, k > 0, and n-dimensional simplified variant ∂t(u )−Δp+1u = 0, where Δp+1u = div (|∇u|p−1∇u). Among the conclusions, we make complete classification of the parameters in the first equation to disti...
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where 0 < α≤ 1, Γ(α) is the gamma function, {A(t) : t ∈ [0,T]} is a family of linear closed operators defined on dense set D(A) in a Banach space E into E, u is the unknown Evalued function, u0 ∈ D(A), and f is a given E-valued function defined on [0,T]. It is assumed that D(A) is independent of t. Let B(E) denote the Banach space of all linear bounded operators in E endowed with the topology d...
متن کاملREGULARITY FOR ENTROPY SOLUTIONS OF PARABOLIC p-LAPLACIAN TYPE EQUATIONS
In this note we give some summability results for entropy solutions of the nonlinear parabolic equation ut − div ap(x,∇u) = f in ]0, T [×Ω with initial datum in L1(Ω) and assuming Dirichlet’s boundary condition, where ap(., .) is a Carathéodory function satisfying the classical Leray-Lions hypotheses, f ∈ L1(]0, T [×Ω) and Ω is a domain in RN . We find spaces of type Lr(0, T ;Mq(Ω)) containing ...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1961
ISSN: 0386-2194
DOI: 10.3792/pja/1195523536