?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Facta.bibl.u-szeged.hu%2F78353%2F&rft.title=Existence+and+blow-up+of+global+solutions+for+a+class+of+fractional+Lane-Emden+heat+flow+system&rft.creator=+Ma+Yunxing&rft.creator=+Yuan+Zixia&rft.subject=01.+Term%C3%A9szettudom%C3%A1nyok&rft.subject=01.01.+Matematika&rft.description=In+this+paper%2C+we+consider+a+class+of+Lane%E2%80%93Emden+heat+flow+system+with+the+fractional+Laplacian+ut+%2B+(%E2%88%92%E2%88%86)+2+u+%3D+N1(v)+%2B+f1(x)%2C+(x%2C+t)+%E2%88%88+Q%2C+vt+%2B+(%E2%88%92%E2%88%86)+2+v+%3D+N2(u)+%2B+f2(x)%2C+(x%2C+t)+%E2%88%88+Q%2C+u(x%2C+0)+%3D+a(x)%2C+v(x%2C+0)+%3D+b(x)%2C+x+%E2%88%88+RN%2C+where+0+%3C+%CE%B1+%E2%89%A4+2%2C+N+%E2%89%A5+3%2C+Q+%3A%3D+RN+%C3%97+(0%2C+%2B%E2%88%9E)%2C+fi(x)+%E2%88%88+L+1+loc(RN)+(i+%3D+1%2C+2)+are+nonnegative+functions.+We+study+the+relationship+between+the+existence%2C+blow-up+of+the+global+solutions+for+the+above+system+and+the+indexes+p%2C+q+in+the+nonlinear+terms+N1(v)%2C+N2(u).+Here%2C+we+first+establish+the+existence+and+uniqueness+of+the+global+solutions+in+the+supercritical+case+by+using+Duhamel%E2%80%99s+integral+equivalent+system+and+the+contraction+mapping+principle%2C+and+we+further+obtain+some+relevant+properties+of+the+global+solutions.+Next%2C+in+the+critical+case%2C+we+prove+the+blow-up+of+nonnegative+solutions+for+the+system+by+utilizing+some+heat+kernel+estimates+and+combining+with+proof+by+contradiction.+Finally%2C+by+means+of+the+test+function+method%2C+we+investigate+the+blow-up+of+negative+solutions+for+the+Cauchy+problem+of+a+more+general+higher-order+nonlinear+evolution+system+with+the+fractional+Laplacian+in+the+subcritical+case.&rft.date=2022&rft.type=Foly%C3%B3irat&rft.type=NonPeerReviewed&rft.format=full&rft.language=hu&rft.identifier=http%3A%2F%2Facta.bibl.u-szeged.hu%2F78353%2F1%2Fejqtde_2022_068.pdf&rft.identifier=+++Ma+Yunxing%3B++Yuan+Zixia%3A+++Existence+and+blow-up+of+global+solutions+for+a+class+of+fractional+Lane-Emden+heat+flow+system.++(2022)+++&rft.language=eng