{"id":41165,"date":"2024-09-26T10:37:06","date_gmt":"2024-09-26T10:37:06","guid":{"rendered":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%b1%d9%81%d8%aa%d8%a7%d8%b1-%d9%85%d9%86%d9%81%d8%ac%d8%b1-%da%a9%d8%b1%d8%af%d9%86-%d8%a8%d8%af%d9%88\/"},"modified":"2024-09-26T10:37:07","modified_gmt":"2024-09-26T10:37:07","slug":"%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%b1%d9%81%d8%aa%d8%a7%d8%b1-%d9%85%d9%86%d9%81%d8%ac%d8%b1-%da%a9%d8%b1%d8%af%d9%86-%d8%a8%d8%af%d9%88","status":"publish","type":"product","link":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%b1%d9%81%d8%aa%d8%a7%d8%b1-%d9%85%d9%86%d9%81%d8%ac%d8%b1-%da%a9%d8%b1%d8%af%d9%86-%d8%a8%d8%af%d9%88\/","title":{"rendered":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0631\u0641\u062a\u0627\u0631 \u0645\u0646\u0641\u062c\u0631 \u06a9\u0631\u062f\u0646 \u0628\u062f\u0648\u0646 \u0639\u0644\u0627\u0645\u062a \u0628\u0631\u0627\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u06af\u0631\u0645\u0627\u06cc \u0646\u06cc\u0645\u0647 \u062e\u0637\u06cc \u0628\u0627 \u063a\u06cc\u0631\u062e\u0637\u06cc \u0628\u0648\u062f\u0646 \u063a\u06cc\u0631 \u0645\u062a\u0646\u0627\u0642\u0636"},"content":{"rendered":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nAsymptotic blow-up behavior for the semilinear heat equation with non scale invariant nonlinearity<\/td>\n<\/tr>\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0631\u0641\u062a\u0627\u0631 \u0645\u0646\u0641\u062c\u0631 \u06a9\u0631\u062f\u0646 \u0628\u062f\u0648\u0646 \u0639\u0644\u0627\u0645\u062a \u0628\u0631\u0627\u06cc \u0645\u0639\u0627\u062f\u0644\u0647 \u06af\u0631\u0645\u0627\u06cc \u0646\u06cc\u0645\u0647 \u062e\u0637\u06cc \u0628\u0627 \u063a\u06cc\u0631\u062e\u0637\u06cc \u0628\u0648\u062f\u0646 \u063a\u06cc\u0631 \u0645\u062a\u0646\u0627\u0642\u0636<\/td>\n<\/tr>\n
\u0646\u0648\u06cc\u0633\u0646\u062f\u06af\u0627\u0646 <\/td>\nDamagui Loth<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nPDF<\/td>\n<\/tr>\n
\u0632\u0628\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u062a\u062d\u0648\u06cc\u0644\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u062a\u0631\u062c\u0645\u0647 \u0634\u062f\u0647 <\/td>\n\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\n<\/tr>\n
\u0646\u062d\u0648\u0647 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 <\/td>\n\u062f\u0648 \u062a\u0627 \u0633\u0647 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634 (\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u062f\u0627\u0646\u0644\u0648\u062f\u06cc)<\/td>\n<\/tr>\n
\u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a<\/td>\n19<\/td>\n<\/tr>\n
\u0644\u06cc\u0646\u06a9 \u062f\u0627\u0646\u0644\u0648\u062f \u0631\u0627\u06cc\u06af\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc<\/td>\n\u062f\u0627\u0646\u0644\u0648\u062f \u0645\u0642\u0627\u0644\u0647<\/a><\/td>\n<\/tr>\n
\u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0645\u0648\u0636\u0648\u0639\u0627\u062a <\/td>\nAnalysis of PDEs,\u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 PDES ,<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a <\/td>\nSubmitted 19 September, 2024; originally announced September 2024.<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u0627\u0631\u0633\u0627\u0644 \u0634\u062f\u0647 \u062f\u0631 19 \u0633\u067e\u062a\u0627\u0645\u0628\u0631 2024 \u061b\u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0633\u067e\u062a\u0627\u0645\u0628\u0631 2024 \u0627\u0639\u0644\u0627\u0645 \u0634\u062f.<\/td>\n<\/tr>\n
\u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u062f\u0631 \u067e\u0627\u06cc\u06af\u0627\u0647 \u0647\u0627\u06cc \u0639\u0644\u0645\u06cc <\/td>\n\n INSPIRE HEP<\/a>
\n
\n NASA ADS<\/a>
\n
\n Google Scholar<\/a>
\n
\n Semantic Scholar<\/a>
\n
\n arXiv<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n

\u0686\u06a9\u06cc\u062f\u0647<\/h2>\n

We characterize the asymptotic behavior near blowup points for positive solutions of the semilinear heat equation \\begin{equation*} \\partial_t u-\u0394u =f(u), \\end{equation*} for nonlinearities which are genuinely non scale invariant, unlike in the standard case $f(u)=u^p$. Indeed, our results apply to a large class of nonlinearities of the form $f(u)=u^pL(u)$, where $p>1$ is Sobolev subcritical and $L$ is a slowly varying function at infinity (which includes for instance logarithms and their powers and iterates, as well as some strongly oscillating functions). More precisely, denoting by $\u03c8$ the unique positive solution of the corresponding ODE $y'(t)=f(y(t))$ which blows up at the same time $T$, we show that if $a\\in\u03a9$ is a blowup point of $u$, then \\begin{equation*} \\lim_{t\\to T}\\frac{u(a+y\\sqrt{T-t},t)}{\u03c8(t)}= 1,\\quad \\text{uniformly for $y$ bounded.} \\end{equation*} Additional blow-up properties are obtained, including the compactness of the blow-up set for the Cauchy problem with decaying initial data.<\/p>\n

\u0686\u06a9\u06cc\u062f\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc (\u062a\u0631\u062c\u0645\u0647 \u0645\u0627\u0634\u06cc\u0646\u06cc)<\/h2>\n

\u0645\u0627 \u0631\u0641\u062a\u0627\u0631 \u0645\u062c\u0627\u0646\u0628\u06cc \u0631\u0627 \u062f\u0631 \u0646\u0632\u062f\u06cc\u06a9\u06cc \u0646\u0642\u0627\u0637 \u0645\u0646\u0641\u062c\u0631 \u0628\u0631\u0627\u06cc \u0631\u0627\u0647 \u062d\u0644 \u0647\u0627\u06cc \u0645\u062b\u0628\u062a \u0645\u0639\u0627\u062f\u0644\u0647 \u06af\u0631\u0645\u0627\u06cc \u0646\u06cc\u0645\u0647 \u062e\u0637\u06cc \u062a\u0648\u0635\u06cc\u0641 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \\ start {\u0645\u0639\u0627\u062f\u0644\u0647*} \\ partial_t u-\u0394U = f (u) \u060c \\ end {\u0645\u0639\u0627\u062f\u0644\u0647*} \u0628\u0631\u0627\u06cc \u063a\u06cc\u0631\u062e\u0637\u06cc \u06a9\u0647 \u0648\u0627\u0642\u0639\u0627\u064b \u063a\u06cc\u0631\u0642\u0627\u0646\u0648\u0646\u06cc \u0647\u0633\u062a\u0646\u062f \u060c \u0628\u062f\u0648\u0646 \u0622\u0646\u06a9\u0647 \u062f\u0631 \u0645\u0642\u06cc\u0627\u0633 \u063a\u06cc\u0631\u0642\u0627\u0646\u0648\u0646\u06cc \u0628\u0627\u0634\u0646\u062f.\u0645\u0648\u0631\u062f \u0627\u0633\u062a\u0627\u0646\u062f\u0627\u0631\u062f $ f (u) = u^p $.\u062f\u0631 \u0648\u0627\u0642\u0639 \u060c \u0646\u062a\u0627\u06cc\u062c \u0645\u0627 \u062f\u0631 \u0645\u0648\u0631\u062f \u06a9\u0644\u0627\u0633 \u0628\u0632\u0631\u06af\u06cc \u0627\u0632 \u063a\u06cc\u0631\u062e\u0637\u06cc \u0647\u0627\u06cc \u0641\u0631\u0645 $ f (u) = u^pl (u) $ \u0627\u0639\u0645\u0627\u0644 \u0645\u06cc \u0634\u0648\u062f \u060c \u06a9\u0647 \u062f\u0631 \u0622\u0646 $ p> 1 $ sobolev subcritical \u0648 $ l $ \u06cc\u06a9 \u0639\u0645\u0644\u06a9\u0631\u062f \u0628\u0647 \u0622\u0631\u0627\u0645\u06cc \u0645\u062a\u0641\u0627\u0648\u062a \u062f\u0631 Infinity \u0627\u0633\u062a (\u06a9\u0647\u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644 \u0644\u06af\u0627\u0631\u06cc\u062a\u0645 \u0647\u0627 \u0648 \u0642\u062f\u0631\u062a \u0648 \u062a\u06a9\u0631\u0627\u0631 \u0622\u0646\u0647\u0627 \u0648 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0628\u0631\u062e\u06cc \u0627\u0632 \u062a\u0648\u0627\u0628\u0639 \u0628\u0647 \u0634\u062f\u062a \u0646\u0648\u0633\u0627\u0646) \u0631\u0627 \u0634\u0627\u0645\u0644 \u0645\u06cc \u0634\u0648\u062f.\u0628\u0647 \u0637\u0648\u0631 \u062f\u0642\u06cc\u0642 \u062a\u0631 \u060c \u0628\u0627 \u0628\u06cc\u0627\u0646 $ \u03c8 $ \u0631\u0627\u0647 \u062d\u0644 \u0645\u062b\u0628\u062a \u0645\u0646\u062d\u0635\u0631 \u0628\u0647 \u0641\u0631\u062f Ode $ y ‘(t) = f (y (t)) $ \u06a9\u0647 \u0647\u0645\u0632\u0645\u0627\u0646 \u0628\u0627 $ t $ \u0645\u0646\u0641\u062c\u0631 \u0645\u06cc \u0634\u0648\u062f \u060c \u0645\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u06a9\u0647 \u0627\u06af\u0631 $ a \\ in\u03a9$ \u06cc\u06a9 \u0646\u0642\u0637\u0647 \u0645\u0646\u0641\u062c\u0631 \u0627\u0632 $ u $ \u0627\u0633\u062a \u060c \u0633\u067e\u0633 \\ start {\u0645\u0639\u0627\u062f\u0644\u0647*} \\ lim_ {t \\ to t} \\ frac {u (a+y \\ sqrt {t-t} \u060c t)} {\u03c8 (t)} = 1\u060c \\ quad \\ text {\u0628\u0647 \u0637\u0648\u0631 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a \u0628\u0631\u0627\u06cc $ y $ \u0645\u062d\u062f\u0648\u062f \u0634\u062f\u0647.} \\ end {\u0645\u0639\u0627\u062f\u0644\u0647*letives \u062e\u0635\u0648\u0635\u06cc\u0627\u062a \u0627\u0646\u0641\u062c\u0627\u0631 \u0627\u0636\u0627\u0641\u06cc \u0628\u0647 \u062f\u0633\u062a \u0645\u06cc \u0622\u06cc\u062f \u060c \u0627\u0632 \u062c\u0645\u0644\u0647 \u0641\u0634\u0631\u062f\u06af\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u0645\u0646\u0641\u062c\u0631 \u0634\u062f\u0647 \u0628\u0631\u0627\u06cc \u0645\u0634\u06a9\u0644 Cauchy \u0628\u0627 \u067e\u0648\u0633\u06cc\u062f\u06af\u06cc \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0627\u0648\u0644\u06cc\u0647.<\/p>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n","protected":false},"excerpt":{"rendered":"

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