Mild solutions to semilinear rough partial differential equations [PDF]
arXivWe provide an existence and uniqueness result for mild solutions to rough partial differential equations in the framework of the semigroup approach. Applications to stochastic partial differential equations driven by infinite dimensional Wiener processes and infinite dimensional fractional Brownian motion are presented as well.
arxiv
On the lack of exact controllability for mild solutions in Banach spaces
Journal of Mathematical Analysis and Applications, 1975 AbstractIt is shown that exact controllability in finite time for linear control systems given on an infinite dimensional separable Banach space in integral form (mild solution) can never arise using locally L1-controls, if the operator through which the control acts on the system is compact.
openaire +2 more sources
Inhibition of Corrosion of Mild Steel in Aqueous Solution of Chloride by Chromate [PDF]
, 1988 SOMNATH SANYAL, B. SANYAL
openalex +1 more source
Annals of Clinical and Translational Neurology, EarlyView.Abstract Objective Exploring the prevalence and association between intracranial atherosclerosis (ICAS) and cerebral small vessel diseases (CSVD), this study delved beyond the current scope, utilising high‐resolution vessel wall MRI (HRVW‐MRI) to investigate how subtle changes in intracranial atherosclerotic features influence the various burdens of ...
Joseph Amihere Ackah +6 more
wiley +1 more source
Uniqueness of mild solutions to the Navier-Stokes equations in weak-type $L^d$ space [PDF]
arXivThis paper deals with the uniqueness of mild solutions to the forced or unforced Navier-Stokes equations in the whole space. It is known that the uniqueness of mild solutions to the unforced Navier-Stokes equations holds in $L^{\infty}(0,T;L^d(\mathbb{R}^d))$ when $d\geq 4$, and in $C([0,T];L^d(\mathbb{R}^d))$ when $d\geq3$.
arxiv
On the Existence of a Global Mild Solution for a Nonlinear Integrodifferential Equation with a Singular Kernel [PDF]
, 1994 J. Heikonen
openalex +1 more source
Progressive Myoclonus Epilepsy: Distinctive MRI Changes in Cerebellar and Motor Networks
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective Progressive myoclonus epilepsy (PME) is a rare generalized epilepsy syndrome with a well‐characterized genetic basis. The brain networks that are affected to give rise to the distinctive symptoms of PME are less well understood. Methods Eleven individuals with PME with a confirmed genetic diagnosis and 22 controls were studied.
Jillian M. Cameron +3 more
wiley +1 more source
Existence and uniqueness of mild solutions for a class of psi-Caputo time-fractional systems of order from one to two [PDF]
arXivWe prove the existence and uniqueness of mild solutions for a specific class of time-fractional $\psi$-Caputo evolution systems with a derivative order ranging from 1 to 2 in Banach spaces. By using the properties of cosine and sine family operators, along with the generalized Laplace transform, we derive a more concise expression for the mild solution.
arxiv
Mild solutions are weak solutions in a class of (non)linear measure-valued evolution equations on a bounded domain [PDF]
arXiv, 2016 We study the connection between mild and weak solutions for a class of measure-valued evolution equations on the bounded domain $[0,1]$. Mass moves, driven by a velocity field that is either a function of the spatial variable only, $v=v(x)$, or depends on the solution $\mu$ itself: $v=v[\mu](x)$.
arxiv
Novel Phenotypes and Deep Intronic Variant Expand TH‐Associated Dopa‐Responsive Dystonia Spectrum
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Approximately 20% of dopa‐responsive dystonia (DRD) cases remain genetically unresolved. Using whole‐genome sequencing, we identified two TH variants in a young DRD patient, including a novel deep intronic variant. Minigene assays confirmed that this variant causes aberrant splicing.
Xiaosheng Zheng +6 more
wiley +1 more source