Matches in SemOpenAlex for { <https://semopenalex.org/work/W2890997989> ?p ?o ?g. }
Showing items 1 to 85 of
85
with 100 items per page.
- W2890997989 abstract "Let $D$ be a bounded $C^2$-domain. Consider the following Dirichlet initial-boundary problem of nonlocal operators with a drift: $$ partial_t u={mathscr L}^{(alpha)}_kappa u+bcdot nabla u+f mathrm{in} mathbb R_+times u|_{mathbb R_+times D^c}=0, u(0,cdot)|_{D}=varphi, $$ where $alphain(0,2)$ and $mathscr L^{(alpha)}_kappa$ is an $alpha$-stable-like nonlocal operator with kernel function $kappa(x,z)$ bounded from above and below by positive constants, and $b:mathbb R^dtomathbb R^d$ is a bounded $C^beta$-function with $alpha+beta>1$, $f: mathbb R_+times Dtomathbb R$ is a $C^gamma$-function in $D$ uniformly in $t$ with $gammain((1-alpha)vee 0,beta]$, $varphiin C^{alpha+gamma}(D)$. Under some Holder assumptions on $kappa$, we show the existence of a unique classical solution $uin L^infty_{loc}(mathbb R_+; C^{alpha+gamma}_{loc}(D))times C(mathbb R_+; C_b(D))$ to the above problem. Moreover, we establish the following probabilistic representation for $u$ $$ u(t,x)=mathbb E_x Big(varphi(X_{t}){bf 1}_{tau_{D}>t}Big)+mathbb E_xleft(int^{twedgetau_{D}}_0f(t-s,X_s){rm d} sright), tgeq 0, xin D, $$ where $((X_t)_{tgeq 0},mathbb P_x; xinmathbb R^d)$ is the Markov process associated with the operator $mathscr L^{(alpha)}_kappa+bcdot nabla$, and $tau_D$ is the first exit time of $X$ from $D$. In the sub and critical case $alphain[1,2)$, the kernel function $kappa$ can be rough in $z$. In the supercritical case $alphain(0,1)$, we classify the boundary points according to the sign of $b(z)cdotvec{n}(z)$, where $zinpartial D$ and $vec{n}(z)$ is the unit outward normal vector. Finally, we provide an example and simulate it by Monte-Carlo method to show our results." @default.
- W2890997989 created "2018-09-27" @default.
- W2890997989 creator A5036882585 @default.
- W2890997989 creator A5089672343 @default.
- W2890997989 date "2018-09-15" @default.
- W2890997989 modified "2023-09-27" @default.
- W2890997989 title "Dirichlet problem for supercritical nonlocal operators" @default.
- W2890997989 cites W1581147332 @default.
- W2890997989 cites W1963638692 @default.
- W2890997989 cites W1980126905 @default.
- W2890997989 cites W1995655627 @default.
- W2890997989 cites W2068042821 @default.
- W2890997989 cites W2078534604 @default.
- W2890997989 cites W2081877251 @default.
- W2890997989 cites W2090275940 @default.
- W2890997989 cites W2099627699 @default.
- W2890997989 cites W2103953214 @default.
- W2890997989 cites W2115441540 @default.
- W2890997989 cites W2126794261 @default.
- W2890997989 cites W2136343001 @default.
- W2890997989 cites W2169071224 @default.
- W2890997989 cites W2342303253 @default.
- W2890997989 cites W2467268925 @default.
- W2890997989 cites W2755120322 @default.
- W2890997989 cites W2765918482 @default.
- W2890997989 cites W2903083557 @default.
- W2890997989 cites W2963206760 @default.
- W2890997989 cites W2963729625 @default.
- W2890997989 cites W2964241717 @default.
- W2890997989 cites W3102061997 @default.
- W2890997989 cites W362850445 @default.
- W2890997989 hasPublicationYear "2018" @default.
- W2890997989 type Work @default.
- W2890997989 sameAs 2890997989 @default.
- W2890997989 citedByCount "5" @default.
- W2890997989 countsByYear W28909979892018 @default.
- W2890997989 countsByYear W28909979892019 @default.
- W2890997989 countsByYear W28909979892020 @default.
- W2890997989 crossrefType "posted-content" @default.
- W2890997989 hasAuthorship W2890997989A5036882585 @default.
- W2890997989 hasAuthorship W2890997989A5089672343 @default.
- W2890997989 hasConcept C114614502 @default.
- W2890997989 hasConcept C121332964 @default.
- W2890997989 hasConcept C134306372 @default.
- W2890997989 hasConcept C2779557605 @default.
- W2890997989 hasConcept C33923547 @default.
- W2890997989 hasConcept C34388435 @default.
- W2890997989 hasConcept C36503486 @default.
- W2890997989 hasConcept C54207081 @default.
- W2890997989 hasConcept C62520636 @default.
- W2890997989 hasConceptScore W2890997989C114614502 @default.
- W2890997989 hasConceptScore W2890997989C121332964 @default.
- W2890997989 hasConceptScore W2890997989C134306372 @default.
- W2890997989 hasConceptScore W2890997989C2779557605 @default.
- W2890997989 hasConceptScore W2890997989C33923547 @default.
- W2890997989 hasConceptScore W2890997989C34388435 @default.
- W2890997989 hasConceptScore W2890997989C36503486 @default.
- W2890997989 hasConceptScore W2890997989C54207081 @default.
- W2890997989 hasConceptScore W2890997989C62520636 @default.
- W2890997989 hasLocation W28909979891 @default.
- W2890997989 hasOpenAccess W2890997989 @default.
- W2890997989 hasPrimaryLocation W28909979891 @default.
- W2890997989 hasRelatedWork W1548195820 @default.
- W2890997989 hasRelatedWork W1630586266 @default.
- W2890997989 hasRelatedWork W166242285 @default.
- W2890997989 hasRelatedWork W2506877683 @default.
- W2890997989 hasRelatedWork W2755120322 @default.
- W2890997989 hasRelatedWork W2784873346 @default.
- W2890997989 hasRelatedWork W2789280914 @default.
- W2890997989 hasRelatedWork W2904954286 @default.
- W2890997989 hasRelatedWork W2953338897 @default.
- W2890997989 hasRelatedWork W2964246254 @default.
- W2890997989 hasRelatedWork W2964276101 @default.
- W2890997989 hasRelatedWork W2999388242 @default.
- W2890997989 hasRelatedWork W3007478402 @default.
- W2890997989 hasRelatedWork W3017032477 @default.
- W2890997989 hasRelatedWork W3030776908 @default.
- W2890997989 hasRelatedWork W3091399206 @default.
- W2890997989 hasRelatedWork W3100714336 @default.
- W2890997989 hasRelatedWork W3169166070 @default.
- W2890997989 hasRelatedWork W3210710693 @default.
- W2890997989 isParatext "false" @default.
- W2890997989 isRetracted "false" @default.
- W2890997989 magId "2890997989" @default.
- W2890997989 workType "article" @default.